cp's OEIS Frontend

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

%I A090748 #72 Mar 09 2025 13:13:49
%S A090748 1,2,4,6,12,16,18,30,60,88,106,126,520,606,1278,2202,2280,3216,4252,
%T A090748 4422,9688,9940,11212,19936,21700,23208,44496,86242,110502,132048,
%U A090748 216090,756838,859432,1257786,1398268,2976220,3021376,6972592,13466916,20996010,24036582,25964950,30402456,32582656
%N A090748 Numbers k such that 2^(k+1) - 1 is prime.
%C A090748 Perfect numbers A000396(n) = 2^A133033(n) - 2^a(n), assuming there are no odd perfect numbers. - _Omar E. Pol_, Feb 24 2008
%C A090748 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
%C A090748 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
%C A090748 Number of 0's in binary expansion of n-th even perfect number (see A135650). - _Omar E. Pol_, May 04 2008
%H A090748 Amiram Eldar, <a href="/A090748/b090748.txt">Table of n, a(n) for n = 1..48</a> (terms 1..47 from Ivan Panchenko)
%H A090748 Omar E. Pol, <a href="http://www.polprimos.com">Determinacion geometrica de los numeros primos y perfectos</a>.
%F A090748 a(n) = A000043(n) - 1.
%F A090748 2^(a(n) + 1) = A051027(2^a(n)). - _Juri-Stepan Gerasimov_, Aug 21 2016 [corrected by _Jerzy R Borysowicz_, Feb 26 2025]
%e A090748 1 is in the sequence because 2^2 - 1 = 3 is prime.
%t A090748 Select[Range[0, 10^4], PrimeQ[2^(# + 1) - 1] &] (* _Vincenzo Librandi_, Jul 28 2016 *)
%o A090748 (Magma) [n: n in [1..5*10^3] |IsPrime(2^(n+1)-1)]; // _Vincenzo Librandi_, Jul 28 2016
%o A090748 (PARI) is(n)=ispseudoprime(2^(n+1)-1) \\ _Charles R Greathouse IV_, Aug 21 2016
%Y A090748 a(n) = A000043(n) - 1. A000043 is the main entry for this sequence.
%Y A090748 Cf. A000396, A133033, A000668, A019279, A061652, A135650, A051027.
%K A090748 nonn
%O A090748 1,2
%A A090748 Mohammed Bouayoun (bouyao(AT)wanadoo.fr), Feb 03 2004
%E A090748 Edited, corrected and extended by _Robert G. Wilson v_, Feb 09 2004
%E A090748 a(39) from _Omar E. Pol_, Jan 23 2009
%E A090748 a(40)-a(44) from _Ivan Panchenko_, Apr 11 2018