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A127936
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Numbers n such that 1 + Sum_{i=1..n} [2^(2i-1)] is prime.
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13
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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
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OFFSET
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1,2
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COMMENTS
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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. [From M. F. Hasler, Aug 29 2008]
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LINKS
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Table of n, a(n) for n=1..40.
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FORMULA
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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, Aug 29 2008]
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EXAMPLE
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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;
...
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MATHEMATICA
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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
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PROG
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(PARI) for(n=1, 999, ispseudoprime(2^(2*n+1)\3+1) & print1(n", ")) \ [From 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
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CROSSREFS
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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 * A096276 A239091 A075725
Adjacent sequences: A127933 A127934 A127935 * A127937 A127938 A127939
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KEYWORD
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nonn,more
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AUTHOR
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Artur Jasinski, Feb 08 2007, Feb 09 2007
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EXTENSIONS
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Edited by N. J. A. Sloane at the suggestion of Andrew 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
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STATUS
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approved
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