A267721 - OEIS

%I #42 Apr 09 2016 17:14:25

%S 3137,199211,523541,16691693,1393313963,2428124317,3498135023,

%T 7318973237,4028940343,191353191413,221327221393,507217507289,

%U 937253937331,10402271040311,843911844001,25654632565559,81661078166209,55778515577959,82237498223863

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

%C Subsequence of A030461.

%C 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 Jean-Marc Rebert, <a href="/A267721/b267721.txt">Table of n, a(n) for n = 1..32</a>

%e a(1) = A030461(2) = 3137. gap =  37 - 31 = 6 = 6 * 1.

%e a(2) = 199211, because 199211 is the first term in A030461, with gap = 211 - 199 = 12 = 6 * 2.

%p Primes:= select(isprime,[seq(i,i=3..10^7,2)]):

%p cati:= (x,y) -> 10^(1+ilog10(y))*x+y;

%p for i from 1 to nops(Primes)-1 do

%p   g:= Primes[i+1]-Primes[i];

%p   if g mod 6 <> 0 then next fi;

%p   if assigned(A[g/6]) then next fi;

%p   z:= cati(Primes[i],Primes[i+1]);

%p   if isprime(z) then A[g/6]:= z fi;

%p od:

%p seq(A[i],i=1..max(map(op,[indices(A)]))); # _Robert Israel_, Jan 24 2016

%Y Cf. A030459, A030460, A030461, A058193, A267692.

%K base,nonn

%O 1,1

%A _Jean-Marc Rebert_, Jan 20 2016