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Search: id:A030124
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| A030124 |
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Complement (and also first differences) of Hofstadter's sequence A005228. |
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+0
17
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| 2, 4, 5, 6, 8, 9, 10, 11, 13, 14, 15, 16, 17, 19, 20, 21, 22, 23, 24, 25, 27, 28, 29, 30, 31, 32, 33, 34, 36, 37, 38, 39, 40, 41, 42, 43, 44, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 70, 71, 72, 73, 74, 75, 76, 77, 78
(list; graph; listen)
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OFFSET
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0,1
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COMMENT
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For any n, all integers k satisfying sum(i=1,n,a(i))+1<k<sum(i=1,n+1,a(i))+1 are in the sequence. E.g. sum(i=1,3,a(i))+1=12, sum(i=1,4,a(i))+1=18, hence 13,14,15,16,17 are in the sequence. - Benoit Cloitre (benoit7848c(AT)orange.fr), Apr 01 2002
The asymptotic equivalence a(n) ~ n follows from the fact that the values disallowed in the present sequence because they occur in A005228 are negligible, since A005228 grows much faster than A030124. The next-to-leading term in the formula is calculated from the functional equation F(x) + G(x) = x, suggested by D. Wilson (cf. reference), where F and G are the inverse functions of smooth, increasing approximations f and f' of A005228 and A030124. It seems that higher order corrections calculated from this equation do not agree with the real behaviour of a(n). - M. F. Hasler (www.univ-ag.fr/~mhasler), Jun 04 2008
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REFERENCES
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E. Angelini, "Jeux de suites", in Dossier Pour La Science, pp. 32-35, Volume 59 (Jeux math'), April/June 2008, Paris.
Hofstadter, "Goedel, Escher, Bach", p. 73.
D. W. Wilson, "Asymptotics about A005228", Posting Jun 03 2008 on SeqFan mailing list (www.seqfan.eu).
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LINKS
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T. D. Noe, Table of n, a(n) for n=0..1000
N. J. A. Sloane, My favorite integer sequences, in Sequences and their Applications (Proceedings of SETA '98).
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
Index entries for sequences from "Goedel, Escher, Bach"
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FORMULA
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A030124(n) = n + sqrt(2n) + o(n^(1/2)) - M. F. Hasler (www.univ-ag.fr/~mhasler), Jun 04 2008
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PROGRAM
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(PARI) a=b=t=1; for(i=1, 100, while(bittest(t, b++), ); print1(b", "); t+=1<<b+1<<a+=b) - M. F. Hasler (www.univ-ag.fr/~mhasler), Jun 04 2008
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CROSSREFS
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Adjacent sequences: A030121 A030122 A030123 this_sequence A030125 A030126 A030127
Sequence in context: A080240 A135668 A039138 this_sequence A064318 A039100 A141204
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KEYWORD
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nonn
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AUTHOR
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Eric Weisstein (eric(AT)weisstein.com)
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