Search: id:A127936
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%I A127936
%S A127936 1,2,3,5,6,8,9,11,15,21,30,39,50,63,83,95,99,156,173,350,854,1308,1769,
%T A127936 2903,5250,5345,5639,6195,7239,21368,41669,47684,58619,63515,69468,
%U A127936 70539,133508,134993,187160,493095
%N A127936 Numbers n such that 1 + Sum_{i=1..n} [2^(2i-1)] is prime.
%C A127936 If this sequence is infinite then so is A124401.
%C A127936 Equals A127965(n)/2.
%C A127936 The sum has the simple closed form 1 + 2/3*(4^n-1). - Stefan Steinerberger 
               (stefan.steinerberger(AT)gmail.com), Nov 24 2007
%C A127936 Terms beyond a(30) correspond to probable primes, cf. A000978. [From 
               M. F. Hasler (Maximilian.Hasler(AT)gmail.com), Aug 29 2008]
%F A127936 a(n) = floor[ A000978(n)/2 ] = ceil( log[4](A000979(n))) ; A000978(n) 
               = 2 a(n) + 1 ; A000979(n) = (2*4^a(n)+1)/3. [From M. F. Hasler (Maximilian.Hasler(AT)gmail.com), 
               Aug 29 2008]
%e A127936 a(1)=1 because 1 + 2 = 3 is prime;
%e A127936 a(2)=2 because 1 + 2 + 2^3 = 11 is prime;
%e A127936 a(3)=3 because 1 + 2 + 2^3 + 2^5 = 43 is prime;
%e A127936 a(4)=5 because 1 + 2 + 2^3 + 2^5 + 2^7 + 2^9 = 683 is prime;
%e A127936 ...
%p A127936 a = {}; Do[If[PrimeQ[1 + Sum[2^(2n - 1), {n, 1, x}]], AppendTo[a, x]], 
               {x, 1, 1000}]; a
%t A127936 b = {}; Do[c = 1 + Sum[2^(2n - 1), {n, 1, x}]; If[PrimeQ[c], AppendTo[b, 
               c]], {x, 0, 1000}]; a = {}; Do[AppendTo[a, FromDigits[IntegerDigits[b[[x]], 
               2]]], {x, 1, Length[b]}]; d = {}; Do[AppendTo[d, (1/2)(DigitCount[a[[x]], 
               10, 0]+DigitCount[a[[x]], 10, 1]]), {x, 1, Length[a]}]; d
%o A127936 (PARI) for(n=1,999, ispseudoprime(2^(2*n+1)\3+1) & print1(n",")) \ [From 
               M. F. Hasler (Maximilian.Hasler(AT)gmail.com), Aug 29 2008]
%Y A127936 Cf. A127962, A127963, A127964, A127965, A127961, A000979, A000978, A124400, 
               A126614, A127955, A127956, A127957, A127958, A127936.
%Y A127936 Cf. A127936, A124401.
%Y A127936 Sequence in context: A000534 A136112 A135768 this_sequence A096276 A075725 
               A049407
%Y A127936 Adjacent sequences: A127933 A127934 A127935 this_sequence A127937 A127938 
               A127939
%K A127936 nonn,more
%O A127936 1,2
%A A127936 Artur Jasinski (grafix(AT)csl.pl), Feb 08 2007, Feb 09 2007
%E A127936 Edited by N. J. A. Sloane (njas(AT)research.att.com) at the suggestion 
               of Andrew Plewe, Jun 11 2007
%E A127936 2 more terms from Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), 
               Nov 24 2007
%E A127936 6 more terms from Dmitry Kamenetsky (dkamen(AT)rsise.anu.edu.au), Jul 
               12 2008
%E A127936 a(30)-a(40) calculated from A000978 by M. F. Hasler (Maximilian.Hasler(AT)gmail.com), 
               Aug 29 2008

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