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.

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, 6, 20, 25, 18, 128, 3, 2, 10, 7, 7, 26, 39, 30, 256, 6, 15, 4, 20, 19, 11, 50, 55, 36, 512, 1, 10, 27, 9, 28, 21, 14, 52, 75, 41, 1024, 1, 4, 46, 51, 10, 82, 43, 17, 92, 85, 66, 2048

Offset: 1

Author

Lorenzo Sauras Altuzarra, Mar 01 2023

Keywords

• nonn
• tabl

Comments

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

Examples

			Table starts
  1   2   4   8  16  32  64 128 ... A000079
  1   2   5   6   8  12  18  30 ... A002253
  1   3   7  13  15  25  39  55 ... A002254
  2   4   6  14  20  26  50  52 ... A032353
  1   2   3   6   7  11  14  17 ... A002256
  1   3   5   7  19  21  43  81 ... A002261
  2   8  10  20  28  82 188 308 ... A032356
  1   2   4   9  10  12  27  37 ... A002258
  ...
(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.
		

Links

• Ray Ballinger and Wilfrid Keller, List of primes k.2^n + 1 for k < 300.

Crossrefs

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

Cf. A033809 (1st column).

Cf. A000004, A046067, A279709.

Programs

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;
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