A361076 - OEIS

A361076

Array, read by ascending antidiagonals, whose n-th row consists of the powers of 2, if n = 1; of the primes of the form (2*n-1)*2^k+1, if they exist and n > 1; and of zeros otherwise.

%I #50 Apr 01 2023 23:57:01

%S 1,1,2,1,2,4,2,3,5,8,1,4,7,6,16,1,2,6,13,8,32,2,3,3,14,15,12,64,1,8,5,

%T 6,20,25,18,128,3,2,10,7,7,26,39,30,256,6,15,4,20,19,11,50,55,36,512,

%U 1,10,27,9,28,21,14,52,75,41,1024,1,4,46,51,10,82,43,17,92,85,66,2048

%N Array, read by ascending antidiagonals, whose n-th row consists of the powers of 2, if n = 1; of the primes of the form (2*n-1)*2^k+1, if they exist and n > 1; and of zeros otherwise.

%C Is a(n) <= A279709(n)?

%H Ray Ballinger and Wilfrid Keller, <a href="http://www.prothsearch.com/riesel1.html">List of primes k.2^n + 1 for k < 300</a>.

%e Table starts

%e 1 2 4 8 16 32 64 128 ... A000079

%e 1 2 5 6 8 12 18 30 ... A002253

%e 1 3 7 13 15 25 39 55 ... A002254

%e 2 4 6 14 20 26 50 52 ... A032353

%e 1 2 3 6 7 11 14 17 ... A002256

%e 1 3 5 7 19 21 43 81 ... A002261

%e 2 8 10 20 28 82 188 308 ... A032356

%e 1 2 4 9 10 12 27 37 ... A002258

%e ...

%e (2*39279 - 1)*2^r + 1 is composite for every r > 0 (see comments from A046067), so the 39279th row is A000004, the zero sequence.

%o (PARI) vk(k, nn) = if (k==1, return (vector(nn, i, 2^(i-1)))); my(v = vector(nn-k+1), nb=0, i=0, x); while (nb != nn-k+1, if (isprime((2*k-1)*2^i+1), nb++; v[nb] = i); i++;); v;

%o lista(nn) = my(v=vector(nn, k, vk(k, nn))); my(w=List()); for (i=1, nn, for (j=1, i, listput(w, v[i-j+1][j]););); Vec(w); \\ _Michel Marcus_, Mar 03 2023

%Y Cf. A000079, A002253, A002254, A032353, A002256, A002261, A032356, A002258.

%Y Cf. A033809 (1st column).

%Y Cf. A000004, A046067, A279709.

%K nonn,tabl

%O 1,3

%A _Lorenzo Sauras Altuzarra_, Mar 01 2023