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Search: id:A127936
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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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+0
10
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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
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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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 (stefan.steinerberger(AT)gmail.com), Nov 24 2007
Terms beyond a(30) correspond to probable primes, cf. A000978. [From M. F. Hasler (Maximilian.Hasler(AT)gmail.com), Aug 29 2008]
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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 (Maximilian.Hasler(AT)gmail.com), 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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MAPLE
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a = {}; Do[If[PrimeQ[1 + Sum[2^(2n - 1), {n, 1, x}]], AppendTo[a, x]], {x, 1, 1000}]; a
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MATHEMATICA
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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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PROGRAM
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(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]
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CROSSREFS
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Cf. A127962, A127963, A127964, A127965, A127961, A000979, A000978, A124400, A126614, A127955, A127956, A127957, A127958, A127936.
Cf. A127936, A124401.
Sequence in context: A000534 A136112 A135768 this_sequence A096276 A075725 A049407
Adjacent sequences: A127933 A127934 A127935 this_sequence 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 (grafix(AT)csl.pl), Feb 08 2007, Feb 09 2007
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EXTENSIONS
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Edited by N. J. A. Sloane (njas(AT)research.att.com) at the suggestion of Andrew Plewe, Jun 11 2007
2 more terms from Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Nov 24 2007
6 more terms from Dmitry Kamenetsky (dkamen(AT)rsise.anu.edu.au), Jul 12 2008
a(30)-a(40) calculated from A000978 by M. F. Hasler (Maximilian.Hasler(AT)gmail.com), Aug 29 2008
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