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A022007 Initial members of prime 5-tuples (p, p+4, p+6, p+10, p+12). 78
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
Zak Seidov, Table of n, a(n) for n = 1..10000 (first 1000 terms from T. D. Noe)
T. Forbes and Norman Luhn, Prime k-tuplets.
Eric Weisstein's World of Mathematics, Prime Constellation.
Wikipedia, Prime k-tuple.
FORMULA
a(n) = 7 + 30*A089157(n). - Zak Seidov, 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
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
Sequence in context: A188441 A178808 A083083 * A174516 A058805 A305137
KEYWORD
nonn,easy
AUTHOR
STATUS
approved

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Last modified May 24 05:24 EDT 2024. Contains 372772 sequences. (Running on oeis4.)