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Search: id:A093094
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| A093094 |
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"Products into digits": start with a(1)=2, a(2)=2; adjoin digits of product of a(k) and a(k+1) for k from 1 to infinity. |
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+0
5
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| 2, 2, 4, 8, 3, 2, 2, 4, 6, 4, 8, 2, 4, 2, 4, 3, 2, 1, 6, 8, 8, 8, 1, 2, 6, 2, 6, 4, 8, 6, 4, 6, 4, 8, 2, 1, 2, 1, 2, 1, 2, 2, 4, 3, 2, 4, 8, 2, 4, 2, 4, 2, 4, 3, 2, 1, 6, 2, 2, 2, 2, 2, 2, 4, 8, 1, 2, 6, 8, 3, 2, 1, 6, 8, 8, 8, 8, 8, 1, 2, 6, 2, 6, 1, 2, 4, 4, 4, 4, 4, 8, 3, 2, 8, 2, 1, 2, 4, 8, 2, 4
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Only the digits 1,2,3,4,6,8 occur, infinitely often. The sequence is not periodic. Around a(800) there are many 8's.
Comment from Giovanni Resta (g.resta(AT)iit.cnr.it), Mar 16 2006: "Proof that sequence is not periodic:
"Let us assume that somewhere in the sequence there is a subsequence of 3 adjacent 8': ...,8,8,8,....(which is true).
"Then we know that in the following there will be the subsequence ...,6,4,6,4.. (i.e. 8x8, 8x8) again, there will be somewhere ...,2,4,2,4,2,4,... (i.e. 6x4, 4x6, 6x4) and finally ...,8,8,8,8,8,...
"Analogously, starting from 8,8,8,8 we obtain 6,4,6,4,6,4 then 2,4,2,4,2,4,2,4,2,4 and finally 8,8,8,8,8,8,8,8,8.
"Generalizing, if somewhere appears a run of k>2 8's, then in some future position will appear a run of at least 4*k-7 8's (where since k>2, 4*k-7>k).
"So the sequence will contain arbitrary long runs of 8's, without being constantly equal to 8, thus it cannot be periodic."
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EXAMPLE
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a(3)=a(1)*a(2), a(4)=a(2)*a(3), a(5)=first digit of (a(3)*a(4)), a(6)=2nd digit of (a(3)*a(4)), a(9)=a(6)*a(7)
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CROSSREFS
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Cf. A093086-A093091.
Sequence in context: A065844 A131199 A112059 this_sequence A045777 A136534 A121175
Adjacent sequences: A093091 A093092 A093093 this_sequence A093095 A093096 A093097
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KEYWORD
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nonn,base
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AUTHOR
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Bodo Zinser (BodoZinser(AT)CosmoData.net), Mar 20 2004
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EXTENSIONS
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Definition revised by Franklin T. Adams-Watters, Mar 16 2006
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