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%I #24 Feb 23 2019 04:44:04
%S 1249,14293,17929,31741,32089,33151,35869,57193,60859,64891,71443,
%T 85303,87481,90793,93103,98533,99679,99961,108079,131221,135319,
%U 139429,140731,144451,157639,165559,171439,175909,180043,186619,193153,203353,214531,217489
%N The smallest of four consecutive primes with prime gaps {a,b,c} = {10,18,2}.
%C 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.
%H Robert Israel, <a href="/A215719/b215719.txt">Table of n, a(n) for n = 1..4147</a>
%e 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}.
%p N:= 10^6; # to get all terms <= 6*N
%p Primes1:= select(isprime,{seq(6*i+1,i=1..N+5)}):
%p Primes5:= select(isprime,{seq(6*i+5,i=1..N+5)}):
%p Q:= `intersect`(Primes1, map(t->t-10, Primes5), map(t->t-28,Primes5), map(t->t-30,Primes1):
%p A215719:= select(t -> select(isprime,{seq(t+2*i,i=1..13)}) = {t+10}, Q): # _Robert Israel_, May 04 2014
%Y Cf. A078858.
%K nonn
%O 1,1
%A _V.J. Pohjola_, Aug 22 2012
%E Definition and comment corrected by _Robert Israel_, May 04 2014
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