A361744 A(n,k) is the least m such that there are k primes in the set {prime(n) + 2^i | 1 <= i <= m}, or -1 if no such number exists; square array A(n,k), n > 1, k >= 1, read by antidiagonals.

1, 2, 1, 3, 3, 2, 4, 5, 4, 1, 6, 11, 6, 3, 2, 7, 47, 8, 5, 4, 1, 12, 53, 10, 7, 8, 13, 2, 15, 141, 16, 9, 20, 21, 6, 3, 16, 143, 18, 15, 38, 33, 30, 7, 1, 18, 191, 20, 23, 64, 81, 162, 39, 3, 4, 28, 273, 28, 29, 80, 129, 654, 79, 5, 12, 2

Offset: 2

Author

Jean-Marc Rebert, Mar 22 2023

Keywords

• nonn
• tabl

Examples

			p = prime(2) = 3, m=1, u = {p + 2^k | 1 <= k <= m} = {5} contains one prime, and no lesser m satisfies this, so A(2,1) = 1.
Square array A(n,k) n > 1 and k >= 1 begins:
 1,     2,     3,     4,     6,     7,    12,    15,    16,    18, ...
 1,     3,     5,    11,    47,    53,   141,   143,   191,   273, ...
 2,     4,     6,     8,    10,    16,    18,    20,    28,    30, ...
 1,     3,     5,     7,     9,    15,    23,    29,    31,    55, ...
 2,     4,     8,    20,    38,    64,    80,   292,  1132,  4108, ...
 1,    13,    21,    33,    81,   129,   285,   297,   769,  3381, ...
 2,     6,    30,   162,   654,   714,  1370,  1662,  1722,  2810, ...
 3,     7,    39,    79,   359,   451,  1031,  1039, 11311, 30227, ...
 1,     3,     5,     7,     9,    13,    15,    17,    23,    27, ...
		

Crossrefs

Cf. A057732 (1st row), A094076 (1st column).

Cf. A361679.

Cf. A019434 (primes 2^n+1), A057732 (2^n+3), A059242 (2^n+5), A057195 (2^n+7), A057196(2^n+9), A102633 (2^n+11), A102634 (2^n+13), A057197 (2^n+15), A057200 (2^n+17), A057221 (2^n+19), A057201 (2^n+21), A057203 (2^n+23).

Cf. A205558 and A231232 (with 2*k instead of 2^k).

Programs

PARI

A(n, k)= {my(nb=0, p=prime(n), m=1); while (nb