

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



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



KEYWORD

nonn,more


AUTHOR



EXTENSIONS



STATUS

approved



