

A335889


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


0



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
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OFFSET

1,2


LINKS

Table of n, a(n) for n=1..39.
Chris K. Caldwell and G. L. Honaker, Jr., Prime Curio for 756839


EXAMPLE

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).


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 *)


CROSSREFS

Cf. A000043, A000396, A000668.
Sequence in context: A186492 A137448 A240606 * A324379 A035165 A290256
Adjacent sequences: A335886 A335887 A335888 * A335890 A335891 A335892


KEYWORD

nonn,more


AUTHOR

G. L. Honaker, Jr., Jun 28 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


STATUS

approved



