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A157891 Number of natural numbers between exponents of successive Mersenne primes. 0

%I #5 May 09 2020 12:43:42

%S 0,1,1,5,3,1,11,29,27,17,19,393,85,671,923,77,935,1035,169,5265,251,

%T 1271,8723,1763,1507,21287,41745,24259,21545,84041,540747,102593,

%U 398353,140481,1577951,45155,3951215,6494323

%N Number of natural numbers between exponents of successive Mersenne primes.

%C 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).

%F a(n) = (A000043(n+1)-A000043(n))-1. [From _Jonathan Vos Post_, Mar 09 2009]

%t Differences[MersennePrimeExponent[Range[40]]]-1 (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, May 09 2020 *)

%Y Cf. A000027, A000043, A046933

%K nonn

%O 1,4

%A _Jani Melik_, Mar 08 2009, Mar 09 2009

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Last modified March 28 20:05 EDT 2024. Contains 371254 sequences. (Running on oeis4.)