Son, we live in a world that has chemicals, and those chemicals have to be stored in un-inspected, leaky tanks. Who's gonna do it? You? The EPA? I have a greater responsibility than you could possibly fathom. You weep for Charleston, WV, and you curse the corporations. You have that luxury. You have the luxury of not knowing what I know. That Charleston, WV's death, while tragic, probably saved lives. And my existence, while grotesque and incomprehensible to you, saves lives. You don't want the truth because deep down in places you don't talk about at parties, you want me on that tank, you need me on that tank. We use words like honor, code, loyalty. We use these words as the backbone of a life spent defending capitalism. You use them as a punchline. I have neither the time nor the inclination to explain myself to a man who rises and sleeps under the blanket of the very products that I provide, and then questions the manner in which I provide it. I would rather you just said thank you, and went on your way, Otherwise, I suggest you start a company, and show me how to store chemicals. Either way, I don't give a damn what you think you are entitled to.
Thursday, January 23, 2014
Monday, January 20, 2014
two consecutive numbers in an additive series plus an offset is equal to the larger numbers n value plus one to the size of the series.
Figured out the relationship between two consecutive numbers in a series and the next larger series. It has to do with multiples of the triangular numbers.
https://github.com/BuckRogers1965/Examples/blob/master/Math/additiveSeries/additiveSeries-Relationships.c
As you can see in the following example program:
https://github.com/BuckRogers1965/Examples/blob/master/Math/additiveSeries/additiveSeries-Relationships.c
As you can see in the following example program:
#include <stdio.h>
int main () {
int i, j, n, x;
for (x=1; x<20; x++) {
printf("\tFor additive series of size %d\n", x);
printf("\tn\tadd\tseries\tformula\t\tnext\tf(n-1)\tf(n)\toffset\n");
for (i = 1, j = 0, n =1 ; n<10; n++, i+=x ){
j+=i;
printf("\t%d\t%d\t%d\t%d\t\t%d\t%d\t%d\t%d\n", n, i, j, (x*n*n-(x-2)*n)/2,
(x*(n-1)*(n-1)-(x-2)*(n-1))/2 + (x*n*n-(x-2)*n)/2 +(-x*n*n +3*x*n +n*n -3*n -2*x +2)/2,
(x*(n-1)*(n-1)-(x-2)*(n-1))/2, (x*n*n-(x-2)*n)/2, (-x*n*n +3*x*n +n*n -3*n -2*x +2)/2 );
}
printf("\n\n");
}
}
For additive series of size 1
n add series formula next f(n-1) f(n) offset
1 1 1 1 1 0 1 0
2 2 3 3 4 1 3 0
3 3 6 6 9 3 6 0
4 4 10 10 16 6 10 0
5 5 15 15 25 10 15 0
6 6 21 21 36 15 21 0
7 7 28 28 49 21 28 0
8 8 36 36 64 28 36 0
9 9 45 45 81 36 45 0
For additive series of size 2
n add series formula next f(n-1) f(n) offset
1 1 1 1 1 0 1 0
2 3 4 4 5 1 4 0
3 5 9 9 12 4 9 -1
4 7 16 16 22 9 16 -3
5 9 25 25 35 16 25 -6
6 11 36 36 51 25 36 -10
7 13 49 49 70 36 49 -15
8 15 64 64 92 49 64 -21
9 17 81 81 117 64 81 -28
For additive series of size 3
n add series formula next f(n-1) f(n) offset
1 1 1 1 1 0 1 0
2 4 5 5 6 1 5 0
3 7 12 12 15 5 12 -2
4 10 22 22 28 12 22 -6
5 13 35 35 45 22 35 -12
6 16 51 51 66 35 51 -20
7 19 70 70 91 51 70 -30
8 22 92 92 120 70 92 -42
9 25 117 117 153 92 117 -56
For additive series of size 4
n add series formula next f(n-1) f(n) offset
1 1 1 1 1 0 1 0
2 5 6 6 7 1 6 0
3 9 15 15 18 6 15 -3
4 13 28 28 34 15 28 -9
5 17 45 45 55 28 45 -18
6 21 66 66 81 45 66 -30
7 25 91 91 112 66 91 -45
8 29 120 120 148 91 120 -63
9 33 153 153 189 120 153 -84
For additive series of size 5
n add series formula next f(n-1) f(n) offset
1 1 1 1 1 0 1 0
2 6 7 7 8 1 7 0
3 11 18 18 21 7 18 -4
4 16 34 34 40 18 34 -12
5 21 55 55 65 34 55 -24
6 26 81 81 96 55 81 -40
7 31 112 112 133 81 112 -60
8 36 148 148 176 112 148 -84
9 41 189 189 225 148 189 -112
For additive series of size 6
n add series formula next f(n-1) f(n) offset
1 1 1 1 1 0 1 0
2 7 8 8 9 1 8 0
3 13 21 21 24 8 21 -5
4 19 40 40 46 21 40 -15
5 25 65 65 75 40 65 -30
6 31 96 96 111 65 96 -50
7 37 133 133 154 96 133 -75
8 43 176 176 204 133 176 -105
9 49 225 225 261 176 225 -140
For additive series of size 7
n add series formula next f(n-1) f(n) offset
1 1 1 1 1 0 1 0
2 8 9 9 10 1 9 0
3 15 24 24 27 9 24 -6
4 22 46 46 52 24 46 -18
5 29 75 75 85 46 75 -36
6 36 111 111 126 75 111 -60
7 43 154 154 175 111 154 -90
8 50 204 204 232 154 204 -126
9 57 261 261 297 204 261 -168
For additive series of size 8
n add series formula next f(n-1) f(n) offset
1 1 1 1 1 0 1 0
2 9 10 10 11 1 10 0
3 17 27 27 30 10 27 -7
4 25 52 52 58 27 52 -21
5 33 85 85 95 52 85 -42
6 41 126 126 141 85 126 -70
7 49 175 175 196 126 175 -105
8 57 232 232 260 175 232 -147
9 65 297 297 333 232 297 -196
For additive series of size 9
n add series formula next f(n-1) f(n) offset
1 1 1 1 1 0 1 0
2 10 11 11 12 1 11 0
3 19 30 30 33 11 30 -8
4 28 58 58 64 30 58 -24
5 37 95 95 105 58 95 -48
6 46 141 141 156 95 141 -80
7 55 196 196 217 141 196 -120
8 64 260 260 288 196 260 -168
9 73 333 333 369 260 333 -224
For additive series of size 10
n add series formula next f(n-1) f(n) offset
1 1 1 1 1 0 1 0
2 11 12 12 13 1 12 0
3 21 33 33 36 12 33 -9
4 31 64 64 70 33 64 -27
5 41 105 105 115 64 105 -54
6 51 156 156 171 105 156 -90
7 61 217 217 238 156 217 -135
8 71 288 288 316 217 288 -189
9 81 369 369 405 288 369 -252
For additive series of size 11
n add series formula next f(n-1) f(n) offset
1 1 1 1 1 0 1 0
2 12 13 13 14 1 13 0
3 23 36 36 39 13 36 -10
4 34 70 70 76 36 70 -30
5 45 115 115 125 70 115 -60
6 56 171 171 186 115 171 -100
7 67 238 238 259 171 238 -150
8 78 316 316 344 238 316 -210
9 89 405 405 441 316 405 -280
For additive series of size 12
n add series formula next f(n-1) f(n) offset
1 1 1 1 1 0 1 0
2 13 14 14 15 1 14 0
3 25 39 39 42 14 39 -11
4 37 76 76 82 39 76 -33
5 49 125 125 135 76 125 -66
6 61 186 186 201 125 186 -110
7 73 259 259 280 186 259 -165
8 85 344 344 372 259 344 -231
9 97 441 441 477 344 441 -308
For additive series of size 13
n add series formula next f(n-1) f(n) offset
1 1 1 1 1 0 1 0
2 14 15 15 16 1 15 0
3 27 42 42 45 15 42 -12
4 40 82 82 88 42 82 -36
5 53 135 135 145 82 135 -72
6 66 201 201 216 135 201 -120
7 79 280 280 301 201 280 -180
8 92 372 372 400 280 372 -252
9 105 477 477 513 372 477 -336
For additive series of size 14
n add series formula next f(n-1) f(n) offset
1 1 1 1 1 0 1 0
2 15 16 16 17 1 16 0
3 29 45 45 48 16 45 -13
4 43 88 88 94 45 88 -39
5 57 145 145 155 88 145 -78
6 71 216 216 231 145 216 -130
7 85 301 301 322 216 301 -195
8 99 400 400 428 301 400 -273
9 113 513 513 549 400 513 -364
For additive series of size 15
n add series formula next f(n-1) f(n) offset
1 1 1 1 1 0 1 0
2 16 17 17 18 1 17 0
3 31 48 48 51 17 48 -14
4 46 94 94 100 48 94 -42
5 61 155 155 165 94 155 -84
6 76 231 231 246 155 231 -140
7 91 322 322 343 231 322 -210
8 106 428 428 456 322 428 -294
9 121 549 549 585 428 549 -392
For additive series of size 16
n add series formula next f(n-1) f(n) offset
1 1 1 1 1 0 1 0
2 17 18 18 19 1 18 0
3 33 51 51 54 18 51 -15
4 49 100 100 106 51 100 -45
5 65 165 165 175 100 165 -90
6 81 246 246 261 165 246 -150
7 97 343 343 364 246 343 -225
8 113 456 456 484 343 456 -315
9 129 585 585 621 456 585 -420
For additive series of size 17
n add series formula next f(n-1) f(n) offset
1 1 1 1 1 0 1 0
2 18 19 19 20 1 19 0
3 35 54 54 57 19 54 -16
4 52 106 106 112 54 106 -48
5 69 175 175 185 106 175 -96
6 86 261 261 276 175 261 -160
7 103 364 364 385 261 364 -240
8 120 484 484 512 364 484 -336
9 137 621 621 657 484 621 -448
For additive series of size 18
n add series formula next f(n-1) f(n) offset
1 1 1 1 1 0 1 0
2 19 20 20 21 1 20 0
3 37 57 57 60 20 57 -17
4 55 112 112 118 57 112 -51
5 73 185 185 195 112 185 -102
6 91 276 276 291 185 276 -170
7 109 385 385 406 276 385 -255
8 127 512 512 540 385 512 -357
9 145 657 657 693 512 657 -476
For additive series of size 19
n add series formula next f(n-1) f(n) offset
1 1 1 1 1 0 1 0
2 20 21 21 22 1 21 0
3 39 60 60 63 21 60 -18
4 58 118 118 124 60 118 -54
5 77 195 195 205 118 195 -108
6 96 291 291 306 195 291 -180
7 115 406 406 427 291 406 -270
8 134 540 540 568 406 540 -378
9 153 693 693 729 540 693 -504
Wednesday, January 15, 2014
General formula for additive series
I couldn't sleep, so instead I figured out the formulas for a whole family of additive series. (x* n ^2 - (x-2)n )/2 where x is the amount you add each time, starting with one and n is the count of the series. This is a general solution to any fixed addition series counting from one. It was really amazing when I changed the program to work with the next entry in the series and it just worked.
https://github.com/BuckRogers1965/Examples/blob/master/Math/additiveSeries/additiveSeries.c
https://github.com/BuckRogers1965/Examples/blob/master/Math/additiveSeries/additiveSeries.c
#include <stdio.h> int main () { int i, j, n, x; for (x=1; x<20; x++) { printf("for additive series of size %d\n", x); for (i = 1, j = 0, n =1 ; n<10; n++, i+=x ){ j+=i; printf("%d %d %d %d \n", n, i, j, (x*n*n-(x-2)*n)/2); } printf("\n\n"); } }
Output: for additive series of size 1 1 1 1 1 2 2 3 3 3 3 6 6 4 4 10 10 5 5 15 15 6 6 21 21 7 7 28 28 8 8 36 36 9 9 45 45 for additive series of size 2 1 1 1 1 2 3 4 4 3 5 9 9 4 7 16 16 5 9 25 25 6 11 36 36 7 13 49 49 8 15 64 64 9 17 81 81 for additive series of size 3 1 1 1 1 2 4 5 5 3 7 12 12 4 10 22 22 5 13 35 35 6 16 51 51 7 19 70 70 8 22 92 92 9 25 117 117 for additive series of size 4 1 1 1 1 2 5 6 6 3 9 15 15 4 13 28 28 5 17 45 45 6 21 66 66 7 25 91 91 8 29 120 120 9 33 153 153 for additive series of size 5 1 1 1 1 2 6 7 7 3 11 18 18 4 16 34 34 5 21 55 55 6 26 81 81 7 31 112 112 8 36 148 148 9 41 189 189 for additive series of size 6 1 1 1 1 2 7 8 8 3 13 21 21 4 19 40 40 5 25 65 65 6 31 96 96 7 37 133 133 8 43 176 176 9 49 225 225 for additive series of size 7 1 1 1 1 2 8 9 9 3 15 24 24 4 22 46 46 5 29 75 75 6 36 111 111 7 43 154 154 8 50 204 204 9 57 261 261 for additive series of size 8 1 1 1 1 2 9 10 10 3 17 27 27 4 25 52 52 5 33 85 85 6 41 126 126 7 49 175 175 8 57 232 232 9 65 297 297 for additive series of size 9 1 1 1 1 2 10 11 11 3 19 30 30 4 28 58 58 5 37 95 95 6 46 141 141 7 55 196 196 8 64 260 260 9 73 333 333 for additive series of size 10 1 1 1 1 2 11 12 12 3 21 33 33 4 31 64 64 5 41 105 105 6 51 156 156 7 61 217 217 8 71 288 288 9 81 369 369 for additive series of size 11 1 1 1 1 2 12 13 13 3 23 36 36 4 34 70 70 5 45 115 115 6 56 171 171 7 67 238 238 8 78 316 316 9 89 405 405 for additive series of size 12 1 1 1 1 2 13 14 14 3 25 39 39 4 37 76 76 5 49 125 125 6 61 186 186 7 73 259 259 8 85 344 344 9 97 441 441 for additive series of size 13 1 1 1 1 2 14 15 15 3 27 42 42 4 40 82 82 5 53 135 135 6 66 201 201 7 79 280 280 8 92 372 372 9 105 477 477 for additive series of size 14 1 1 1 1 2 15 16 16 3 29 45 45 4 43 88 88 5 57 145 145 6 71 216 216 7 85 301 301 8 99 400 400 9 113 513 513 for additive series of size 15 1 1 1 1 2 16 17 17 3 31 48 48 4 46 94 94 5 61 155 155 6 76 231 231 7 91 322 322 8 106 428 428 9 121 549 549 for additive series of size 16 1 1 1 1 2 17 18 18 3 33 51 51 4 49 100 100 5 65 165 165 6 81 246 246 7 97 343 343 8 113 456 456 9 129 585 585 for additive series of size 17 1 1 1 1 2 18 19 19 3 35 54 54 4 52 106 106 5 69 175 175 6 86 261 261 7 103 364 364 8 120 484 484 9 137 621 621 for additive series of size 18 1 1 1 1 2 19 20 20 3 37 57 57 4 55 112 112 5 73 185 185 6 91 276 276 7 109 385 385 8 127 512 512 9 145 657 657 for additive series of size 19 1 1 1 1 2 20 21 21 3 39 60 60 4 58 118 118 5 77 195 195 6 96 291 291 7 115 406 406 8 134 540 540 9 153 693 693
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