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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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified December 5 04:50 EST 2022. Contains 358578 sequences. (Running on oeis4.)