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Search: id:A096535
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| A096535 |
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a(0) = a(1) = 1; a(n) = (a(n-1) + a(n-2)) mod n. |
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+0
13
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| 1, 1, 0, 1, 1, 2, 3, 5, 0, 5, 5, 10, 3, 0, 3, 3, 6, 9, 15, 5, 0, 5, 5, 10, 15, 0, 15, 15, 2, 17, 19, 5, 24, 29, 19, 13, 32, 8, 2, 10, 12, 22, 34, 13, 3, 16, 19, 35, 6, 41, 47, 37, 32, 16, 48, 9, 1, 10, 11, 21, 32, 53, 23, 13, 36, 49, 19, 1, 20, 21, 41, 62, 31, 20, 51, 71, 46, 40, 8, 48, 56
(list; graph; listen)
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OFFSET
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0,6
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COMMENT
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Suggested by Leroy Quet
Three conjectures: (1) All numbers appear infinitely often, i.e. for every number k >= 0 and every frequency f > 0 there is an index i such that a(i) = k is the f-th occurrence of k in the sequence.
(2) a(j) = a(j-1) + a(j-2) and a(j) = a(j-1) + a(j-2) - j occur approximately equally often, i.e. lim {n -> infinity} x_n / y_n = 1, where x_n is the number of j <= n such that a(j) = a(j-1) + a(j-2) and y_n is the number of j <= n such that a(j) = a(j-1) + a(j-2) - j (cf. A122276).
(3) There are sections a(g+1), ..., a(g+k) of arbitrary length k such that a(g+h) = a(g+h-1) + a(g+h-2) for h = 1,...,k, i.e. the sequence is non-decreasing in these sections (cf. A122277, A122278, A122279). - Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Aug 29 2006
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LINKS
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T. D. Noe, Table of n, a(n) for n=0..10000
Leroy Quet, Home Page (listed in lieu of email address)
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MATHEMATICA
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l = {1, 1}; For[i = 2, i <= 100, i++, len = Length[l]; l = Append[l, Mod[l[[len]] + l[[len - 1]], i]]]; l
f[s_] := f[s] = Append[s, Mod[s[[ -2]] + s[[ -1]], Length[s]]]; Nest[f, {1, 1}, 80] (* Robert G. Wilson v, Aug 29 2006 *)
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CROSSREFS
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Cf. A079777, A096534, A096274 (location of 0's).
Sequence in context: A039705 A082118 A079344 this_sequence A126047 A023049 A062007
Adjacent sequences: A096532 A096533 A096534 this_sequence A096536 A096537 A096538
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KEYWORD
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easy,nonn,nice
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AUTHOR
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Frank Adams-Watters (FrankTAW(AT)Netscape.net), Jun 23 2004
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