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A022007 Initial members of prime quintuplets (p, p+4, p+6, p+10, p+12). 75
7, 97, 1867, 3457, 5647, 15727, 16057, 19417, 43777, 79687, 88807, 101107, 257857, 266677, 276037, 284737, 340927, 354247, 375247, 402757, 419047, 427237, 463447, 470077, 626617, 666427, 736357, 823717, 855727, 959467, 978067, 1022377, 1043587, 1068247 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Subsequence of A052378. - R. J. Mathar, Feb 11 2013

All terms are congruent to 7 (modulo 30). - Matt C. Anderson, May 22 2015

This sequence is related to the admissible prime 5-tuple (0, 4, 6, 10, 12) because the sequence [1, 2, 3, 1, 2, repeat(1)] gives for n >= 1 the smallest element of RS0(A000040(n)) (the smallest nonnegative complete residue systems modulo prime(n)) which defines a residue class containing none of the 5-tuple members. This 5-tuple is one of two prime constellations of diameter 12. The other one is (0, 2, 6, 8, 12) with initial members given in A022006. See the Wikipedia and Weisstein pages. - Wolfdieter Lang, Oct 06 2017

LINKS

T. D. Noe and Moshe Levin, Table of n, a(n) for n = 1..10000 (First 1000 terms from T. D. Noe.)

T. Forbes, Prime k-tuplets

Eric Weisstein's World of Mathematics, Prime Constellation

Wikipedia, Prime k-tuple

FORMULA

a(n) = 7 + 30*A089157(n). - Moshe Levin, Nov 01 2011

EXAMPLE

Admissibility guaranteeing sequence [1, 2, 3, 1, 2, repeat(1)] examples: the only residue class modulo prime(3) = 5 which contains none of the 5-tuple (0, 4, 6, 10, 12) members is 3 (mod 5). For prime(5) = 11 the first class is 2 (mod 11); the others are 3, 5, 7, 8, 9 (mod 11). - Wolfdieter Lang, Oct 06 2017

MATHEMATICA

lst={}; Do[p=Prime[n]; If[PrimeQ[p+4]&&PrimeQ[p+6]&&PrimeQ[p+10]&&PrimeQ[p+12], AppendTo[lst, p]], {n, 9!}]; lst (* Vladimir Joseph Stephan Orlovsky, Sep 25 2008 *)

Transpose[Select[Partition[Prime[Range[76000]], 5, 1], Differences[#] == {4, 2, 4, 2}&]][[1]] (* Harvey P. Dale, Aug 16 2014 *)

PROG

(PARI) forprime(p=2, 1e5, if(isprime(p+4)&&isprime(p+6)&&isprime(p+10)&&isprime(p+12), print1(p", "))) \\ Charles R Greathouse IV, Jul 15 2011

(MAGMA) [p: p in PrimesUpTo(2*10^6) | IsPrime(p+4) and IsPrime(p+6) and IsPrime(p+10)and IsPrime(p+12)]; // Vincenzo Librandi, Aug 23 2015

(Perl) use ntheory ":all"; say for sieve_prime_cluster(1, 1e7, 4, 6, 10, 12); # Dana Jacobsen, Sep 30 2015

CROSSREFS

Cf. A022006, A089157.

Sequence in context: A188441 A178808 A083083 * A174516 A058805 A132061

Adjacent sequences:  A022004 A022005 A022006 * A022008 A022009 A022010

KEYWORD

nonn,easy,changed

AUTHOR

Warut Roonguthai

STATUS

approved

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Last modified October 18 05:05 EDT 2017. Contains 293487 sequences.