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Search: id:A006127
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| A006127 |
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2^n + n.
(Formerly M2547)
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+0
24
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| 1, 3, 6, 11, 20, 37, 70, 135, 264, 521, 1034, 2059, 4108, 8205, 16398, 32783, 65552, 131089, 262162, 524307, 1048596, 2097173, 4194326, 8388631, 16777240, 33554457, 67108890, 134217755, 268435484, 536870941, 1073741854, 2147483679, 4294967328, 8589934625
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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For numbers m=n+2^n such that equation x=2^(m-x) has solution x=2^n, see A103354. - Zak Seidov (zakseidov(AT)yahoo.com), Mar 23 2005
Primes of the form x^x+1 must be of the form 2^2^(a(n))+1, that is, Fermat number F_(a(n)) (Sierpinski 1958). - David W. Wilson (davidwwilson(AT)comcast.net), May 08 2005
a(n) = n-th Mersenne number + n + 1 = A000225(n) + n + 1. Partial sums of a(n) are A132925(n+1), [From Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), Oct 16 2009]
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
John H. Conway, R. K. Guy, The Book of Numbers, Copernicus Press, p. 84.
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LINKS
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S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
S. Plouffe, 1031 Generating Functions and Conjectures, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 435
Eric Weisstein's World of Mathematics, Sierpinski Number of the First Kind
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FORMULA
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Row sums of triangle A135227. - Gary W. Adamson (qntmpkt(AT)yahoo.com), Nov 23 2007
Partial sums of A094373. G.f. : (1-x-x^2)/((1-x)^2(1-2x)) - Paul Barry (pbarry(AT)wit.ie), Aug 05 2004
Binomial transform of [1,2,1,1,1,1,1,...]. - Franklin T. Adams-Watters (FrankTAW(AT)Netscape.net), Nov 29 2006
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MAPLE
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A006127:=(-1+z+z**2)/(2*z-1)/(z-1)**2; [Conjectured by S. Plouffe in his 1992 dissertation.]
g:=1/(1-2*z): gser:=series(g, z=0, 43): seq(coeff(gser, z, n)+n, n=0..34); # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jan 11 2009]
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MATHEMATICA
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s=3; lst={1, s}; Do[s+=(s-n); AppendTo[lst, Abs[s]], {n, 0, 5!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Oct 10 2008]
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CROSSREFS
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Cf. A135227.
Sequence in context: A125896 A094989 A052467 this_sequence A122106 A007707 A018174
Adjacent sequences: A006124 A006125 A006126 this_sequence A006128 A006129 A006130
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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