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A319494
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Triangle of the consecutive absolute differences between consecutive elements of the previous row, first row being the prime numbers (A000040), read by columns.
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0
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2, 1, 3, 1, 2, 1, 5, 0, 1, 2, 2, 1, 7, 2, 2, 1, 4, 0, 2, 1, 11, 2, 0, 2, 1, 2, 0, 0, 2, 1, 13, 2, 0, 0, 2, 1, 4, 0, 0, 0, 0, 1, 17, 2, 0, 0, 2, 0, 1, 2, 0, 0, 2, 0, 0, 1, 19, 2, 0, 2, 2, 0, 0, 1, 4, 0, 2, 0, 0, 0, 0, 1
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OFFSET
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1,1
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COMMENTS
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Gilbreath's conjecture says that the first element of each row except the first row equals 1. - Rémy Sigrist, Nov 15 2018
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LINKS
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EXAMPLE
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1st column
| 2nd column
| | 3rd column
| | | 4th column
v | v | ...
v v
2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 ...
1 2 2 4 2 4 2 4 6 2 6 4 2 4 ...
1 0 2 2 2 2 2 2 4 4 2 2 2 ...
1 2 0 0 0 0 0 2 0 2 0 0 ... .
1 2 0 0 0 0 2 2 2 2 0 ... .
1 2 0 0 0 2 0 0 0 2 ... .
1 2 0 0 2 2 0 0 2 ... .
1 2 0 2 0 2 0 2 ... .
1 2 2 2 2 2 2 ... .
1 0 0 0 0 0 ... .
1 0 0 0 0 ... .
1 0 0 0 ... .
1 0 0 ... .
1 0 ... .
1 ... .
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PROG
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(PARI) T(n, k) = {if (k==n, return (prime(n))); abs(T(n, k+1) - T(n-1, k)); }
tabl(nn) = for (n=1, nn, for (k=1, n, print1(T(n, k), ", ")); print); \\ Michel Marcus, Oct 28 2018
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CROSSREFS
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First row consists of the prime numbers (A000040).
Second row gives the absolute values of differences between consecutive primes (A001223).
Third row gives the absolute values of second differences between primes (A036263 in absolute value).
Fourth row gives the absolute values of differences of absolute values of second differences between primes (A036272).
...
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KEYWORD
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AUTHOR
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STATUS
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approved
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