A335889 a(n) is the number of Mersenne primes between consecutive perfect numbers.

1, 2, 0, 3, 1, 0, 0, 3, 1, 0, 0, 2, 0, 3, 2, 1, 0, 0, 0, 3, 0, 2, 1, 0, 1, 1, 2, 1, 0, 0, 4, 0, 0, 0, 2, 0, 2, 3, 3

Offset: 1

Author

G. L. Honaker, Jr., Jun 28 2020

Keywords

• nonn
• more

Examples

			a(1) = 1 because there is exactly 1 Mersenne prime (7) between the first and second perfect numbers (6 and 28).
a(4) = 3 because there are exactly 3 Mersenne primes (8191, 131071, 524287) between the fourth and fifth perfect numbers (8128 and 33550336).
		

Links

• Chris K. Caldwell and G. L. Honaker, Jr., Prime Curio for 756839

Crossrefs

Cf. A000043, A000396, A000668.

Programs

Mathematica

p = MersennePrimeExponent @ Range[47];mer[p_] := 2^p - 1; perf[p_] := mer[p] * 2^(p - 1); mers = mer /@ p; perfs = Select[perf /@ p, # < mers[[-1]] &]; BinCounts[mers, {perfs}] (* Amiram Eldar, Jun 29 2020 *)

Extensions

a(5)-a(13) from Metin Sariyar, Jun 28 2020

a(14)-a(16) and a(20)-a(39) from Metin Sariyar, Jun 29 2020

a(17)-a(19) from Amiram Eldar, Jun 29 2020