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Search: id:A121319
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| A121319 |
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a(n) is the smallest number k such that k and 2^k have the same last n digits. Here k must have at least n digits (cf. A113627). |
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4
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| 14, 36, 736, 8736, 48736, 948736, 2948736, 32948736, 432948736, 3432948736, 53432948736, 353432948736, 5353432948736, 75353432948736, 1075353432948736, 5075353432948736, 15075353432948736, 615075353432948736, 8615075353432948736, 98615075353432948736
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Note from njas, May 07 2007: some of the comments in this entry may really be referring to A113627.
For n>1, a(n) = the smallest element of A064541 containing at least n decimal digits. - Max Alekseyev, Apr 18 2007
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LINKS
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Jon Schoenfield, Table of n, a(n) for n = 1..80
Jon Schoenfield, Excel program
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FORMULA
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Define b(n) by: b(2) = 36; for n >= 3, b(n) = 2^b(n-1) mod 10^n. This gives A109405. Then if b(n) has n digits, a(n) = b(n), otherwise a(n) = b(n) + 10^n. - Max Alekseyev, May 05 2007
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EXAMPLE
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2^14 = 16384 and 14 end with the same single digit 4, thus a(1) = 14.
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MATHEMATICA
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f[n_] := Block[{k = If[n == 1, 2, 10], m = 10^n}, While[ PowerMod[2, k, m] != Mod[k, m], k += 2]; k]; Do[ Print@f@n, {n, 9}] (* Robert G. Wilson v *)
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PROGRAM
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(PARI) A121319(n) = { local(k, tn); tn=10^n ; forstep(k=2, 1000000000, 2, if ( k % tn == (2^k) % tn, return(k) ; ) ; ) ; return(0) ; } { for(n = 1, 13, print( A121319(n)) ; ) ; } - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Aug 27 2006
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CROSSREFS
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Cf. A007185, A016090, A003226, A035383, A064540, A064541, A109405.
Sequence in context: A024814 A058486 A113627 this_sequence A034181 A057439 A058826
Adjacent sequences: A121316 A121317 A121318 this_sequence A121320 A121321 A121322
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KEYWORD
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nonn,base
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AUTHOR
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Tanya Khovanova (tanyakh(AT)yahoo.com), Aug 25 2006
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EXTENSIONS
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a(6)-a(9) from Robert G. Wilson v and Jon E. Schoenfield (jonscho(AT)hiwaay.net), Aug 26 2006
a(10) from Robert G. Wilson v Sep 26 2006
a(11)-a(16) from Alexander Adamchuk (alex(AT)kolmogorov.com), Jan 28 2007
a(16) corrected by Max Alekseyev, Apr 12 2007
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