A319494 Triangle of the consecutive absolute differences between consecutive elements of the previous row, first row being the prime numbers (A000040), read by columns.
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
Offset: 1
Examples
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 ... .
Links
- Wikipedia, Gilbreath's conjecture
Crossrefs
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).
...
Cf. A036261.
Programs
-
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
Comments