A090748 Numbers n such that 2^(n+1) - 1 is prime.

1, 2, 4, 6, 12, 16, 18, 30, 60, 88, 106, 126, 520, 606, 1278, 2202, 2280, 3216, 4252, 4422, 9688, 9940, 11212, 19936, 21700, 23208, 44496, 86242, 110502, 132048, 216090, 756838, 859432, 1257786, 1398268, 2976220, 3021376, 6972592, 13466916, 20996010, 24036582, 25964950, 30402456, 32582656

Offset

1,2

Comments

Perfect numbers A000396(n) = 2^A133033(n) - 2^a(n), assuming there are no odd perfect numbers. - Omar E. Pol, Feb 24 2008

Number of proper divisors of n-th even perfect number that are multiples of n-th Mersenne prime A000668(n). - Omar E. Pol, Feb 28 2008

Base 2 logarithm of n-th even superperfect number A061652(n). Also base 2 logarithm of n-th superperfect number A019279(n), assuming there are no odd superperfect numbers. - Omar E. Pol, Apr 11 2008

Number of 0's in binary expansion of n-th even perfect number (see A135650). - Omar E. Pol, May 04 2008

Links

Ivan Panchenko, Table of n, a(n) for n = 1..47

Omar E. Pol, Determinacion geometrica de los numeros primos y perfectos.

Formula

2^a(n) = A051027(2^(n+1)). - Juri-Stepan Gerasimov, Aug 21 2016

Example

1 is in the sequence because 2^2 - 1 = 3 is prime.

Mathematica

Select[Range[0, 10^4], PrimeQ[2^(# + 1) - 1] &] (* Vincenzo Librandi, Jul 28 2016

Prog

(Magma) [n: n in [1..5*10^3] |IsPrime(2^(n+1)-1)]; // Vincenzo Librandi, Jul 28 2016
(PARI) is(n)=ispseudoprime(2^(n+1)-1) \\ Charles R Greathouse IV, Aug 21 2016

Crossrefs

a(n) = A000043(n) - 1. A000043 is the main entry for this sequence.

Cf. A000396, A133033, A000668, A019279, A061652, A135650, A051027.

Sequence in context: A260698 A309096 A019280 * A188047 A032465 A089395

Adjacent sequences: A090745 A090746 A090747 * A090749 A090750 A090751

Keyword

nonn

Author

Mohammed Bouayoun (bouyao(AT)wanadoo.fr), Feb 03 2004

Extensions

Edited, corrected and extended by Robert G. Wilson v, Feb 09 2004

Updated (a(39)) by Omar E. Pol, Jan 23 2009

a(40)-a(44) from Ivan Panchenko, Apr 11 2018

Status

approved