A141279 -id:A141279 - cp's OEIS frontend

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.

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 *)

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).

A141272 Number of partitions of n into distinct nonzero Mancala numbers (A007952).

Original entry on oeis.org

1, 0, 1, 1, 1, 1, 0, 1, 2, 1, 1, 2, 1, 2, 2, 1, 3, 2, 1, 3, 3, 2, 2, 2, 3, 4, 2, 2, 5, 4, 3, 4, 5, 5, 4, 4, 5, 7, 4, 3, 8, 7, 5, 6, 6, 8, 9, 5, 7, 12, 7, 7, 10, 8, 11, 9, 8, 14, 13, 9, 12, 16, 13, 13, 13, 14, 18, 14, 12, 17, 19, 14, 16, 20, 17, 20, 19, 18, 25, 21, 18, 25, 24, 21

Offset: 1

Reinhard Zumkeller, Jun 21 2008

nonn

			a(20) = #{17+3, 11+9, 11+5+3+1} = 3;
a(21) = #{21, 17+3+1, 11+9+1} = 3;
a(22) = #{21+1, 17+5} = 2.

Cf. A141271, A141279, A000586.

A141296 Primes p such that p-6^2, p-6, p, p+6 and p+6^2 are consecutive primes.

Original entry on oeis.org

846493, 1407187, 1427963, 3675277, 3750833, 4266673, 4331647, 4346767, 4348307, 4841693, 5952077, 6827237, 7421137, 7470143, 7684483, 7974143, 8569153, 8651543, 8976713, 9073783, 9552083, 11245763, 11459317, 12348997, 12524503

Offset: 1

Rick L. Shepherd, Jun 24 2008

nonn

Equivalently, third of five consecutive primes with this consecutive difference pattern: 30, 6, 6, 30. Subsequence of A141279.

			a(1) = 846493 because 846457, 846487, 846493, 846499 and 846529 are consecutive primes and no smaller primes have this pattern of differences.

Rick L. Shepherd, Table of n, a(n) for n = 1..5200

Cf. A141279, A053070.

Transpose[Select[Partition[Prime[Range[830000]],5,1],Differences[#] == {30,6,6,30}&]] [[3]] (* Harvey P. Dale, Sep 09 2011 *)

cp's OEIS Frontend

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

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A141272 Number of partitions of n into distinct nonzero Mancala numbers (A007952).

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A141296 Primes p such that p-6^2, p-6, p, p+6 and p+6^2 are consecutive primes.

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