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

3137, 199211, 523541, 16691693, 1393313963, 2428124317, 3498135023, 7318973237, 4028940343, 191353191413, 221327221393, 507217507289, 937253937331, 10402271040311, 843911844001, 25654632565559, 81661078166209, 55778515577959, 82237498223863

Offset: 1

Author

Jean-Marc Rebert, Jan 20 2016

Keywords

• base
• nonn

Comments

Subsequence of A030461.

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.

Examples

			a(1) = A030461(2) = 3137. gap =  37 - 31 = 6 = 6 * 1.
a(2) = 199211, because 199211 is the first term in A030461, with gap = 211 - 199 = 12 = 6 * 2.
		

Links

• Jean-Marc Rebert, Table of n, a(n) for n = 1..32

Crossrefs

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

Programs

Maple

Primes:= select(isprime,[seq(i,i=3..10^7,2)]):
cati:= (x,y) -> 10^(1+ilog10(y))*x+y;
for i from 1 to nops(Primes)-1 do
  g:= Primes[i+1]-Primes[i];
  if g mod 6 <> 0 then next fi;
  if assigned(A[g/6]) then next fi;
  z:= cati(Primes[i],Primes[i+1]);
  if isprime(z) then A[g/6]:= z fi;
od:
seq(A[i],i=1..max(map(op,[indices(A)]))); # Robert Israel, Jan 24 2016