A141280 -id:A141280 - cp's OEIS frontend

A141279 Primes p such that p - 6^2, p - 6, p + 6 and p + 6^2 are also primes.

47, 53, 67, 73, 103, 233, 277, 353, 373, 607, 947, 977, 1187, 1223, 1487, 1663, 2683, 2693, 2713, 2963, 3307, 3733, 4457, 5443, 6323, 6863, 7523, 9007, 11903, 11933, 12107, 12547, 12583, 15313, 15767, 18217, 19427, 20107, 20753, 21523, 22073

Offset: 1

Rick L. Shepherd, Jun 21 2008

nonn

Subsequence of A006489. A141280 and A141281 are subsequences.

Rick L. Shepherd, Table of n, a(n) for n = 1..10000

Cf. A006489, A141280, A141281, A141282.

pQ[n_]:=And@@PrimeQ[{n-36,n-6,n+6,n+36}]; Select[Prime[Range[10,3000]],pQ]  (* Harvey P. Dale, Feb 02 2011 *)
Select[Prime[Range[10,3000]],AllTrue[#+{-36,-6,6,36},PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Aug 05 2018 *)

A141281 Primes p such that p-6^4, p-6^3, p-6^2, p-6, p, p+6, p+6^2, p+6^3 and p+6^4 are primes.

Original entry on oeis.org

11459317, 18726137, 73718633, 181975727, 361471043, 374195537, 419533753, 420522673, 428739323, 429198703, 456975157, 483576523, 544795393, 653578573, 682118777, 703313623, 753422317, 764967257, 797492477, 960985037, 1059913073

Offset: 1

Rick L. Shepherd, Jun 22 2008

nonn

Subsequence of A006489, A141279 and A141280. Each term is congruent to 1 or 10 mod 11 so for no prime p can this pattern be extended also to include primes p-6^5 and p+6^5 (one of them is divisible by 11). See A070392 for residues mod 11 of powers of 6. As each term of A006489 greater than 11 is congruent to 3 or 7 mod 10, combining results gives that a(n) is congruent to 23, 43, 67, or 87 mod 110.

Rick L. Shepherd, Table of n, a(n) for n = 1..55

Cf. A006489, A141279, A141280, A141282, A070392.

Select[Prime[Range[53734400]],AllTrue[#+{1296,216,36,6,-6,-36,-216,-1296},PrimeQ]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Apr 01 2021 *)

A141282 Least prime p such that p-6^n, ..., p-6, p, p+6, ... and p+6^n are primes.

Original entry on oeis.org

11, 47, 233, 11459317

Offset: 1

Rick L. Shepherd, Jun 22 2008

This pattern is impossible for n >= 5. See A141281.

			a(4) = 11459317 as this is the least prime p such that p-6^4, p-6^3, p-6^2, p-6, p, p+6, p+6^2, p+6^3 and p+6^4 are all prime. The nine primes are 11458021, 11459101, 11459281, 11459311, 11459317, 11459323, 11459353, 11459533 and 11460613.

Cf. A006489, A141279, A141280, A141281.

a(1) = A006489(1), a(2) = A141279(1), a(3) = A141280(1), a(4) = A141281(1).

cp's OEIS Frontend

A141279 Primes p such that p - 6^2, p - 6, p + 6 and p + 6^2 are also primes.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

A141281 Primes p such that p-6^4, p-6^3, p-6^2, p-6, p, p+6, p+6^2, p+6^3 and p+6^4 are primes.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

A141282 Least prime p such that p-6^n, ..., p-6, p, p+6, ... and p+6^n are primes.

Views

Author

Keywords

Comments

Examples

Crossrefs

Formula