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

1,1

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.

Links

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

Example

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.

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

Crossrefs

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

Sequence in context: A238499 A176790 A086103 * A031554 A180297 A187645

Adjacent sequences: A267718 A267719 A267720 * A267722 A267723 A267724

Keyword

base,nonn

Author

Jean-Marc Rebert, Jan 20 2016

Status

approved