A215719 The smallest of four consecutive primes with prime gaps {a,b,c} = {10,18,2}.

1249, 14293, 17929, 31741, 32089, 33151, 35869, 57193, 60859, 64891, 71443, 85303, 87481, 90793, 93103, 98533, 99679, 99961, 108079, 131221, 135319, 139429, 140731, 144451, 157639, 165559, 171439, 175909, 180043, 186619, 193153, 203353, 214531, 217489

Offset: 1

Author

V.J. Pohjola, Aug 22 2012

Keywords

• nonn

Comments

Conjecture: The terms of any feasible prime gap triple {a,b,c} to form a quadruple of consecutive primes are sums of terms of three consecutive subsequences of the infinite integer sequence with period (4,2,4,2,4,6,2,6). By this token all possible sequences of quadruples of consecutive primes can be generated, including those already in the OEIS.

Examples

			The terms of the prime gap triple {10,18,2} are the sums of the terms of the following (arbitrarily chosen) subsequences ..., {4,2,4}, {6,2,6,4}, {2}, ... For n=3, a(n) = 17929 is the smallest prime of the third prime quadruple {17929, 17939, 17957, 17959}.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..4147

Crossrefs

Cf. A078858.

Programs

Maple

N:= 10^6; # to get all terms <= 6*N
Primes1:= select(isprime,{seq(6*i+1,i=1..N+5)}):
Primes5:= select(isprime,{seq(6*i+5,i=1..N+5)}):
Q:= `intersect`(Primes1, map(t->t-10, Primes5), map(t->t-28,Primes5), map(t->t-30,Primes1):
A215719:= select(t -> select(isprime,{seq(t+2*i,i=1..13)}) = {t+10}, Q): # Robert Israel, May 04 2014

Extensions

Definition and comment corrected by Robert Israel, May 04 2014