A279709 -id:A279709 - cp's OEIS frontend

A279703 Number of n X n 0..1 arrays with no element equal to a strict majority of its horizontal and antidiagonal neighbors and with new values introduced in order 0 sequentially upwards.

1, 2, 11, 125, 3245, 187484, 24137862, 6837220721, 4307342174510, 5994530717421378, 18451958514090493382

Offset: 1

R. H. Hardin, Dec 17 2016

nonn

Diagonal of A279709.

			Some solutions for n=4
..0..1..0..1. .0..1..0..1. .0..1..0..0. .0..1..0..1. .0..1..1..0
..0..1..0..0. .1..0..0..1. .0..1..1..1. .0..1..1..0. .0..0..1..0
..0..1..1..0. .1..0..1..0. .1..0..0..0. .0..0..1..1. .1..0..0..1
..0..0..1..0. .1..0..1..0. .0..1..1..0. .1..0..0..1. .1..1..0..1

Cf. A279709.

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 (2n-1)2^k+1, if they exist and n > 1; and of zeros otherwise.

Original entry on oeis.org

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

Lorenzo Sauras Altuzarra, Mar 01 2023

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

			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.

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

Cf. A000079, A002253, A002254, A032353, A002256, A002261, A032356, A002258.
Cf. A033809 (1st column).
Cf. A000004, A046067, A279709.

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

cp's OEIS Frontend

A279703 Number of n X n 0..1 arrays with no element equal to a strict majority of its horizontal and antidiagonal neighbors and with new values introduced in order 0 sequentially upwards.

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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 (2n-1)2^k+1, if they exist and n > 1; and of zeros otherwise.

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PARI

cp's OEIS Frontend

A279703 Number of n X n 0..1 arrays with no element equal to a strict majority of its horizontal and antidiagonal neighbors and with new values introduced in order 0 sequentially upwards.

Views

Author

Keywords

Comments

Examples

Crossrefs

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.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

PARI

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 (2n-1)2^k+1, if they exist and n > 1; and of zeros otherwise.