This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A127936 Numbers n such that 1 + Sum_{i=1..n} 2^(2i-1) is prime. 13
 1, 2, 3, 5, 6, 8, 9, 11, 15, 21, 30, 39, 50, 63, 83, 95, 99, 156, 173, 350, 854, 1308, 1769, 2903, 5250, 5345, 5639, 6195, 7239, 21368, 41669, 47684, 58619, 63515, 69468, 70539, 133508, 134993, 187160, 493095 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS If this sequence is infinite then so is A124401. Equals A127965(n)/2. The sum has the simple closed form 1 + 2/3*(4^n-1). - Stefan Steinerberger, Nov 24 2007 Terms beyond a(30) correspond to probable primes, cf. A000978. - M. F. Hasler, Aug 29 2008 LINKS FORMULA a(n) = floor(A000978(n)/2) = ceiling(log(4)(A000979(n))); A000978(n) = 2 a(n) + 1; A000979(n) = (2*4^a(n)+1)/3. - M. F. Hasler, Aug 29 2008 EXAMPLE a(1)=1 because 1 + 2 = 3 is prime; a(2)=2 because 1 + 2 + 2^3 = 11 is prime; a(3)=3 because 1 + 2 + 2^3 + 2^5 = 43 is prime; a(4)=5 because 1 + 2 + 2^3 + 2^5 + 2^7 + 2^9 = 683 is prime; ... MATHEMATICA a = {}; Do[If[PrimeQ[1 + Sum[2^(2n - 1), {n, 1, x}]], AppendTo[a, x]], {x, 1, 1000}]; a 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 PROG (PARI) for(n=1, 999, ispseudoprime(2^(2*n+1)\3+1) & print1(n", ")) \\ M. F. Hasler, Aug 29 2008 (Haskell) import Data.List (findIndices) a127936 n = a127936_list !! (n-1) a127936_list = findIndices ((== 1) . a010051'') a007583_list -- Reinhard Zumkeller, Mar 24 2013 (Python) from sympy import isprime A127936 = [i for i in range(1, 10**3) if isprime(int('01'*i+'1', 2))] # Chai Wah Wu, Sep 05 2014 CROSSREFS Cf. A127962, A127963, A127964, A127965, A127961, A000979, A000978, A124400, A126614, A127955, A127956, A127957, A127958, A127936, A127936, A124401, A010051, A007583. Sequence in context: A219729 A000534 A136112 * A280771 A280744 A096276 Adjacent sequences:  A127933 A127934 A127935 * A127937 A127938 A127939 KEYWORD nonn,more AUTHOR Artur Jasinski, Feb 08 2007, Feb 09 2007 EXTENSIONS Edited by N. J. A. Sloane at the suggestion of Andrew S. Plewe, Jun 11 2007 2 more terms from Stefan Steinerberger, Nov 24 2007 6 more terms from Dmitry Kamenetsky, Jul 12 2008 a(30)-a(40) calculated from A000978 by M. F. Hasler, Aug 29 2008 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified October 20 15:29 EDT 2019. Contains 328267 sequences. (Running on oeis4.)