A361484 -id:A361484 - cp's OEIS frontend

A361485 Primes p such that p + 1024 is also prime.

7, 37, 67, 73, 79, 127, 139, 157, 163, 193, 199, 277, 283, 337, 349, 409, 457, 463, 487, 499, 547, 577, 613, 643, 673, 709, 787, 823, 853, 877, 883, 907, 1039, 1063, 1087, 1117, 1129, 1213, 1249, 1327, 1399, 1423, 1453, 1567, 1597, 1609, 1663, 1669, 1753, 1777, 1873, 1879

Offset: 1

Elmo R. Oliveira, Mar 13 2023

All terms are == 1 (mod 6).

			139 and 139 + 1024 = 1163 are both prime.

Winston de Greef, Table of n, a(n) for n = 1..10000

Cf. A000040.

Cf. sequences of the type p + k are primes: A001359 (k = 2), A023200 (k = 4), A023202 (k = 8), A049488 (k = 16), A049489 (k = 32), A049490 (k = 64), A049491 (k = 128), A361483 (k = 256), A361484 (k = 512), this sequence (k = 1024).

lista(nn)=my(v=vector(nn), p=2); for(n=1, nn, until(isprime(p+1024), p=nextprime(p+1)); v[n]=p); v \\ Winston de Greef, Mar 20 2023

A361483 Primes p such that p + 256 is also prime.

Original entry on oeis.org

7, 13, 37, 61, 97, 103, 127, 163, 193, 211, 223, 307, 313, 331, 337, 397, 421, 463, 487, 541, 571, 601, 607, 631, 673, 691, 727, 757, 853, 907, 937, 967, 1021, 1033, 1051, 1063, 1117, 1153, 1171, 1231, 1237, 1297, 1303, 1327, 1381, 1453, 1531, 1567, 1621, 1657, 1693, 1723

Offset: 1

Elmo R. Oliveira, Mar 13 2023

All terms are == 1 (mod 6).

			61 and 61 + 256 = 317 are both prime.

Cf. A000040.

Cf. sequences of the type p + k are primes: A001359 (k = 2), A023200 (k = 4), A023202 (k = 8), A049488 (k = 16), A049489 (k = 32), A049490 (k = 64), A049491 (k = 128), this sequence (k = 256), A361484 (k = 512), A361485 (k = 1024).

A361679 A(n,k) is the n-th prime p such that p + 2^k is also prime; square array A(n,k), n>=1, k>=1, read by antidiagonals.

Original entry on oeis.org

3, 3, 5, 3, 7, 11, 3, 5, 13, 17, 5, 7, 11, 19, 29, 3, 11, 13, 23, 37, 41, 3, 7, 29, 31, 29, 43, 59, 7, 11, 19, 41, 37, 53, 67, 71, 11, 13, 23, 37, 47, 43, 59, 79, 101, 7, 29, 37, 29, 43, 71, 67, 71, 97, 107, 5, 37, 59, 61, 53, 67, 107, 73, 89, 103, 137

Offset: 1

Alois P. Heinz, Mar 20 2023

			Square array A(n,k) begins:
    3,   3,   3,   3,   5,   3,   3,   7,  11,   7, ...
    5,   7,   5,   7,  11,   7,  11,  13,  29,  37, ...
   11,  13,  11,  13,  29,  19,  23,  37,  59,  67, ...
   17,  19,  23,  31,  41,  37,  29,  61,  89,  73, ...
   29,  37,  29,  37,  47,  43,  53,  97, 101,  79, ...
   41,  43,  53,  43,  71,  67,  71, 103, 107, 127, ...
   59,  67,  59,  67, 107,  73,  83, 127, 131, 139, ...
   71,  79,  71,  73, 131, 103, 101, 163, 149, 157, ...
  101,  97,  89,  97, 149, 109, 113, 193, 179, 163, ...
  107, 103, 101, 151, 167, 127, 149, 211, 197, 193, ...

Alois P. Heinz, Antidiagonals n = 1..200, flattened

Columns k=1-10 give: A001359, A023200, A023202, A049488, A049489, A049490, A049491, A361483, A361484, A361485.
Row n=1 gives A056206.
Main diagonal gives A361680.
Cf. A000040.

A:= 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))

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A361485 Primes p such that p + 1024 is also prime.

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A361483 Primes p such that p + 256 is also prime.

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A361679 A(n,k) is the n-th prime p such that p + 2^k is also prime; square array A(n,k), n>=1, k>=1, read by antidiagonals.

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