A319494 - OEIS

A319494

Triangle of the consecutive absolute differences between consecutive elements of the previous row, first row being the prime numbers (A000040), read by columns.

%I #22 Nov 15 2018 15:12:23

%S 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,

%T 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,

%U 2,0,0,0,0,1

%N Triangle of the consecutive absolute differences between consecutive elements of the previous row, first row being the prime numbers (A000040), read by columns.

%C Gilbreath's conjecture says that the first element of each row except the first row equals 1. - _Rémy Sigrist_, Nov 15 2018

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Gilbreath's_conjecture">Gilbreath's conjecture</a>

%e 1st column

%e | 2nd column

%e | | 3rd column

%e | | | 4th column

%e v | v | ...

%e v v

%e 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 ...

%e 1 2 2 4 2 4 2 4 6 2 6 4 2 4 ...

%e 1 0 2 2 2 2 2 2 4 4 2 2 2 ...

%e 1 2 0 0 0 0 0 2 0 2 0 0 ... .

%e 1 2 0 0 0 0 2 2 2 2 0 ... .

%e 1 2 0 0 0 2 0 0 0 2 ... .

%e 1 2 0 0 2 2 0 0 2 ... .

%e 1 2 0 2 0 2 0 2 ... .

%e 1 2 2 2 2 2 2 ... .

%e 1 0 0 0 0 0 ... .

%e 1 0 0 0 0 ... .

%e 1 0 0 0 ... .

%e 1 0 0 ... .

%e 1 0 ... .

%e 1 ... .

%o (PARI) T(n, k) = {if (k==n, return (prime(n))); abs(T(n, k+1) - T(n-1, k));}

%o tabl(nn) = for (n=1, nn, for (k=1, n, print1(T(n,k), ", ")); print); \\ _Michel Marcus_, Oct 28 2018

%Y First row consists of the prime numbers (A000040).

%Y Second row gives the absolute values of differences between consecutive primes (A001223).

%Y Third row gives the absolute values of second differences between primes (A036263 in absolute value).

%Y Fourth row gives the absolute values of differences of absolute values of second differences between primes (A036272).

%Y ...

%Y Cf. A036261.

%K nonn,tabl

%O 1,1

%A _Tristan Cam_, Sep 20 2018