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Search: id:A000012
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| A000012 |
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The simplest sequence of positive numbers: the all 1's sequence.
(Formerly M0003)
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+0
701
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| 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1
(list; table; graph; listen)
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OFFSET
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0,1
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COMMENT
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Number of ways of writing n as a product of primes.
Number of ways of writing n as a sum of distinct powers of 2.
Continued fraction for golden ratio A001622.
Partial sums of A000007 (characteristic function of 0). - Jeremy Gardiner (jeremy.gardiner(AT)btinternet.com), Sep 08 2002
An example of an infinite sequence of positive integers whose distinct pairwise concatenations are all primes! - Don Reble, Apr 17 2005
Binomial transform of A000007; inverse binomial transform of A000079 . Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Jul 07 2005
A063524(a(n)) = 1. [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Oct 11 2008]
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REFERENCES
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Michael Z. Spivey and Laura L. Steil, The k-Binomial Transforms and the Hankel Transform, Journal of Integer Sequences, Vol. 9 (2006), Article 06.1.1.
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LINKS
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N. J. A. Sloane, Table of n, a(n) for n = 0..1000 [Useful when plotting one sequence against another. See Swayne link.]
Daniele A. Gewurz and Francesca Merola, Sequences realized as Parker vectors ..., J. Integer Seqs., Vol. 6, 2003.
N. J. A. Sloane, Illustration of initial terms
D. F. Swayne, Plot pairs of sequences in the OEIS
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics
Eric Weisstein's World of Mathematics, Chromatic Number
Eric Weisstein's World of Mathematics, Graph Cycle
G. Xiao, Contfrac
Index entries for "core" sequences
Index entries for characteristic functions
Index entries for continued fractions for constants
Index entries for related partition-counting sequences
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FORMULA
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G.f.: 1/(1-x); a(n)=1. E.g.f.: e^x.
G.f.: Product[(1+x^(2^k)),{k,0,Infinity}]. - Zak Seidov (zakseidov@yahoo.com), Apr 06 2007
Multiplicative with a(p^e) = 1.
Dirichlet generating function: zeta(s). - Franklin T. Adams-Watters, Sep 11 2005.
Regarded as a square array by antidiagonals, g.f. 1/((1-x)(1-y)), e.g.f. sum T(n,m) x^n/n! y^m/m! = e^{x+y}, e.g.f. sum T(n,m) x^n y^m/m! = e^y/(1-x). Regarded as a triangular array, g.f. 1/((1-x)(1-xy)), e.g.f. sum T(n,m) x^n y^m/m! = e^{xy}/(1-x). - Frank Adams-Watters (FrankTAW(AT)Netscape.net), Feb 06 2006
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MAPLE
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A000012 := n->1;
[ seq(1, i=0..100) ];
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MATHEMATICA
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a[n_] := 1
Array[1 &, 50] - Joseph Biberstine (jrbibers(AT)indiana.edu), Dec 26 2006
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PROGRAM
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(MAGMA) [ 1 : n in [0..100]];
(PARI) a(n)=1
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CROSSREFS
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Cf. A000004, A007395, A010701.
Adjacent sequences: A000009 A000010 A000011 this_sequence A000013 A000014 A000015
Sequence in context: A077008 A087960 A114523 this_sequence A008836 A064179 A106400
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KEYWORD
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core,easy,nonn,mult,cofr,tabl
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AUTHOR
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njas
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