A141281 -id:A141281 - 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 *)

A141280 Primes p such that p-6^3, p-6^2, p-6, p, p+6, p+6^2 and p+6^3 are primes.

Original entry on oeis.org

233, 353, 977, 1663, 2693, 4457, 5443, 11933, 20107, 23333, 23893, 41263, 108923, 110813, 294347, 554633, 730783, 748603, 851387, 928643, 1005013, 1008193, 1020043, 1150873, 1194763, 1326313, 1427963, 1477103, 2161337, 2212003

Offset: 1

Rick L. Shepherd, Jun 21 2008

nonn

Subsequence of A006489 and A141279. A141281 is a subsequence.

Rick L. Shepherd, Table of n, a(n) for n = 1..1000

Cf. A006489, A141279, A141281, A141282.

p6Q[n_]:=With[{c=6^Range[3]},AllTrue[Join[n+c,n-c],PrimeQ]]; Select[ Prime[ Range[ 50,200000]],p6Q] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Jun 06 2015 *)

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.

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A141280 Primes p such that p-6^3, p-6^2, p-6, p, p+6, p+6^2 and p+6^3 are primes.

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

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