|
|
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
|
|
|
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
|
|
|
|