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A157891
Number of natural numbers between exponents of successive Mersenne primes.
1
0, 1, 1, 5, 3, 1, 11, 29, 27, 17, 19, 393, 85, 671, 923, 77, 935, 1035, 169, 5265, 251, 1271, 8723, 1763, 1507, 21287, 41745, 24259, 21545, 84041, 540747, 102593, 398353, 140481, 1577951, 45155, 3951215, 6494323, 7529093, 3040571, 1928367, 4437505, 2180199, 4574009
OFFSET
1,4
LINKS
FORMULA
a(n) = (A000043(n+1)-A000043(n))-1. - Jonathan Vos Post, Mar 09 2009
EXAMPLE
a(0) = 0 since 2 is adjacent to 3 (exponent of 2nd Mersenne prime).
a(2) = 1 since 4 is between 3 and 5 (exponent of 3rd Mersenne prime).
a(3) = 1 since 6 is between 5 and 7 (exponent of 4th Mersenne prime).
a(4) = 5 since 8, 9, 10, 11, and 12 are between 7 and 13 (exponent 5th Mersenne prime).
MATHEMATICA
Differences[MersennePrimeExponent[Range[40]]]-1 (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, May 09 2020 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Jani Melik, Mar 08 2009, Mar 09 2009
EXTENSIONS
a(39)-a(44) from Amiram Eldar, Oct 18 2024
STATUS
approved