

A215719


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


1



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
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OFFSET

1,1


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.


LINKS

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


EXAMPLE

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}.


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>t10, Primes5), map(t>t28, Primes5), map(t>t30, Primes1):
A215719:= select(t > select(isprime, {seq(t+2*i, i=1..13)}) = {t+10}, Q): # Robert Israel, May 04 2014


CROSSREFS

Cf. A078858.
Sequence in context: A233222 A020384 A086709 * A120376 A231805 A122272
Adjacent sequences: A215716 A215717 A215718 * A215720 A215721 A215722


KEYWORD

nonn


AUTHOR

V.J. Pohjola, Aug 22 2012


EXTENSIONS

Definition and comment corrected by Robert Israel, May 04 2014


STATUS

approved



