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A151752
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a(n) = the unique n-digit number with all digits odd that is divisible by 5^n.
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2
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5, 75, 375, 9375, 59375, 359375, 3359375, 93359375, 193359375, 3193359375, 73193359375, 773193359375, 3773193359375, 73773193359375, 773773193359375, 5773773193359375, 15773773193359375, 515773773193359375, 7515773773193359375
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| Another way to phrase the proof of uniqueness: after we take the last n-1 digits to be the previous number in the sequence, all odd possibilities for the first digit give different remainders mod 5. By pigeon hole principle, exactly one of them generates the required number. - Tanya Khovanova, Jun 18, 2009
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FORMULA
| a(n) = d(n)*10^(n-1) + a(n-1), where d(n), the leading digit of a(n), is one of the odd digits 1, 3, 5, 7, or 9 (forming the complete set of residues modulo 5) and is uniquely defined by the congruence: d(n) == (- a(n-1) / 10^(n-1)) (mod 5). [From Max Alekseyev]
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MAPLE
| a:= proc(n) option remember; local k, l; if n=1 then 5 else l:= a(n-1); for k from 1 to 9 by 2 while (parse (cat(k, l)) mod 5^n)<>0 do od; parse (cat(k, l)) fi end: seq (a(n), n=1..30); # Alois P. Heinz, Jun 18 2009
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MATHEMATICA
| nxt[n_]:=Module[{x=FromDigits/@(Prepend[IntegerDigits[n], # ]&/@{1, 3, 5, 7, 9}), l}, l=IntegerLength[n]+1; First[Select[x, Mod[ #, 5^l]==0&]]]; NestList[nxt, 5, 25] [From Harvey P. Dale, Jul 06 2009
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CROSSREFS
| Cf. A151753, A151754.
Sequence in context: A156703 A048350 A030991 * A127212 A091903 A105490
Adjacent sequences: A151749 A151750 A151751 * A151753 A151754 A151755
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KEYWORD
| nonn,base
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AUTHOR
| David Wilson (davidwwilson(AT)comcast.net), Jun 16 2009
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EXTENSIONS
| More terms from Max Alekseyev (maxale(AT)gmail.com), Jun 17 2009
Further terms from Alois P. Heinz (heinz(AT)hs-heilbronn.de), Jun 18 2009
More terms from Harvey P. Dale (hpd1(AT)nyu.edu), Jul 06 2009
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