cp's OEIS Frontend

A267721 a(n) is the least term of A030461 with gap = 6*n between consecutive primes or 0 if no such term exists.

%I A267721 #42 Apr 09 2016 17:14:25
%S A267721 3137,199211,523541,16691693,1393313963,2428124317,3498135023,
%T A267721 7318973237,4028940343,191353191413,221327221393,507217507289,
%U A267721 937253937331,10402271040311,843911844001,25654632565559,81661078166209,55778515577959,82237498223863
%N A267721 a(n) is the least term of A030461 with gap = 6*n between consecutive primes or 0 if no such term exists.
%C A267721 Subsequence of A030461.
%C A267721 a(n) is the concatenation of the smallest prime p and the next prime q, such that p + 6n = q and the concatenations of these 2 primes is also prime. a(n) = 0 if no such term exists.
%H A267721 Jean-Marc Rebert, <a href="/A267721/b267721.txt">Table of n, a(n) for n = 1..32</a>
%e A267721 a(1) = A030461(2) = 3137. gap =  37 - 31 = 6 = 6 * 1.
%e A267721 a(2) = 199211, because 199211 is the first term in A030461, with gap = 211 - 199 = 12 = 6 * 2.
%p A267721 Primes:= select(isprime,[seq(i,i=3..10^7,2)]):
%p A267721 cati:= (x,y) -> 10^(1+ilog10(y))*x+y;
%p A267721 for i from 1 to nops(Primes)-1 do
%p A267721   g:= Primes[i+1]-Primes[i];
%p A267721   if g mod 6 <> 0 then next fi;
%p A267721   if assigned(A[g/6]) then next fi;
%p A267721   z:= cati(Primes[i],Primes[i+1]);
%p A267721   if isprime(z) then A[g/6]:= z fi;
%p A267721 od:
%p A267721 seq(A[i],i=1..max(map(op,[indices(A)]))); # _Robert Israel_, Jan 24 2016
%Y A267721 Cf. A030459, A030460, A030461, A058193, A267692.
%K A267721 base,nonn
%O A267721 1,1
%A A267721 _Jean-Marc Rebert_, Jan 20 2016