A361679 -id:A361679 - cp's OEIS frontend

A361680 The n-th prime p such that p + 2^n is also prime.

3, 7, 11, 31, 47, 67, 83, 163, 179, 193, 263, 367, 389, 499, 563, 571, 887, 967, 1229, 1087, 1367, 1873, 1289, 2647, 1907, 2083, 1979, 2557, 2267, 3697, 2909, 3121, 3761, 4507, 4373, 4723, 5279, 5857, 6359, 6793, 7727, 8167, 7853, 6823, 6779, 8059, 9479, 10567

Offset: 1

Alois P. Heinz, Mar 20 2023

nonn

This sequence is non-monotonic: a(19) = 1229 > a(20) = 1087.

Alois P. Heinz, Table of n, a(n) for n = 1..1000

Main diagonal of A361679.

Cf. A000040.

b:= proc() option remember; local f; f:= proc() [] end;
      proc(n, k) option remember; local p;
        p:= `if`(nops(f(k))=0, 1, f(k)[-1]);
        while nops(f(k)) b(n$2):
seq(a(n), n=1..55);

a(n) = A361679(n,n).

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.

Original entry on oeis.org

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

Jean-Marc Rebert, Mar 22 2023

			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, ...

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).

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

cp's OEIS Frontend

A361680 The n-th prime p such that p + 2^n is also prime.

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