A254248 Number of terms in A006285 (de Polignac numbers) less than 10^n.

0, 1, 1, 18, 262, 3393, 39541, 421863, 4457974, 46853770, 482301801, 4931928485

Offset: 0

Author

Arkadiusz Wesolowski, Mar 16 2015

Keywords

• nonn
• more

Comments

a(n) < 10^n*exp(-(n*log(10))^c) for some c.

Links

• Carlos Rivera, Puzzle 219. Polignac numbers, The Prime Puzzles and Problems Connection.

Crossrefs

Cf. A006285, A255816, A255971, A256164, A256238.

Programs

Mathematica

dePolignacQ[n_] := OddQ[n] && Module[{m = 2}, While[n > m + 1 && ! PrimeQ[n - m], m *= 2]; n <= m + 1]; seq[max_] := Module[{p = 10, c = 1, s = {0}}, Do[If[dePolignacQ[k], c++]; If[k == p, p *= 10; AppendTo[s, c]], {k, 5, 10^max}]; s]; seq[6] (* Amiram Eldar, Feb 04 2021 *)

Extensions

a(9) from Arkadiusz Wesolowski, Feb 09 2016

a(10)-a(11) from Amiram Eldar, Feb 04 2021