A361483 -id:A361483 - cp's OEIS frontend

A269257 Primes p such that p+2^4, p+2^6 and p+2^8 are all primes.

7, 37, 163, 337, 757, 967, 1033, 1303, 2293, 2377, 2647, 2713, 3607, 5023, 6763, 7417, 8677, 8803, 9157, 9277, 10273, 14683, 14827, 15313, 15667, 16417, 20113, 21163, 21757, 22093, 24907, 27043, 27763, 29803, 29863, 32173, 34897, 36793, 36997, 37783, 38287, 38977, 39607

Offset: 1

Debapriyay Mukhopadhyay, Jul 12 2016

nonn

			The prime 7 is in the sequence because 7+16 = 23, 7+64 = 71 and 7+256 = 263 are all primes.
The prime 37 is in the sequence because 37+16 = 53, 37+64 = 101 and 37+256 = 293 are all primes.

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
Debapriyay Mukhopadhyay, C program to generate the terms of the sequences A269257, A269258, A269259, A269859 and A270203 up to 10^8

Subsequence of A002476, A049488, and A049490.

Select[Prime[Range[10000]], PrimeQ[# + 2^4] && PrimeQ[# + 2^6] && PrimeQ[# + 2^8]&] (* Jean-François Alcover, Jul 12 2016 *)
With[{c=2^Range[4,8,2]},Select[Prime[Range[4200]],AllTrue[#+c,PrimeQ]&]] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, May 21 2017 *)

is(n)=n%6==1 && isprime(n+16) && isprime(n+64) && isprime(n+256) && isprime(n) \\ Charles R Greathouse IV, Jul 12 2016

use ntheory ":all"; say for sieve_prime_cluster(2,1e6, 16,64,256); # Dana Jacobsen, Jul 13 2016

A049488 INTERSECT A049490 INTERSECT A361483. - R. J. Mathar, Mar 26 2024

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

Original entry on oeis.org

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

A361484 Primes p such that p + 512 is also prime.

Original entry on oeis.org

11, 29, 59, 89, 101, 107, 131, 149, 179, 197, 227, 239, 257, 311, 317, 347, 479, 509, 521, 557, 617, 641, 659, 701, 719, 809, 887, 911, 941, 947, 971, 977, 1019, 1031, 1097, 1109, 1151, 1181, 1187, 1229, 1277, 1289, 1319, 1361, 1367, 1439, 1481, 1487, 1499, 1571, 1601

Offset: 1

Elmo R. Oliveira, Mar 13 2023

All terms are == 5 (mod 6).

			59 and 59 + 512 = 571 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), A361483 (k = 256), this sequence (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))

cp's OEIS Frontend

A269257 Primes p such that p+2^4, p+2^6 and p+2^8 are all primes.

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

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PARI

A361484 Primes p such that p + 512 is also prime.

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Comments

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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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