A141282 -id:A141282 - 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 *)

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 *)

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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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.

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