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 A090748 Numbers n such that 2^(n+1) - 1 is prime. 27
 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 (list; graph; refs; listen; history; text; internal format)
 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 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

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Last modified November 13 08:18 EST 2019. Contains 329093 sequences. (Running on oeis4.)