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 A151752 a(n) is the unique n-digit number with all digits odd that is divisible by 5^n. 3
 5, 75, 375, 9375, 59375, 359375, 3359375, 93359375, 193359375, 3193359375, 73193359375, 773193359375, 3773193359375, 73773193359375, 773773193359375, 5773773193359375, 15773773193359375, 515773773193359375, 7515773773193359375, 97515773773193359375 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 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 the pigeonhole principle, exactly one of them generates the required number. - Tanya Khovanova, Jun 18 2009 LINKS Alois P. Heinz, Table of n, a(n) for n = 1..300 33rd USAMO 2003, Problem 1 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). - Max Alekseyev 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 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] (* Harvey P. Dale, Jul 06 2009 *) PROG (Magma) v:=[5]; for i in [2..20] do for s in [1, 3, 5, 7, 9] do v[i]:=s*10^(i-1)+v[i-1]; if v[i] mod 5^i eq 0 then break; end if; end for; end for; v; // Marius A. Burtea, Mar 18 2019 CROSSREFS Cf. A151753, A151754. Sequence in context: A048350 A030991 A216093 * A127212 A091903 A105490 Adjacent sequences: A151749 A151750 A151751 * A151753 A151754 A151755 KEYWORD nonn,base AUTHOR David W. Wilson, Jun 16 2009 EXTENSIONS More terms from Max Alekseyev, Jun 17 2009 Further terms from Alois P. Heinz, Jun 18 2009 More terms from Harvey P. Dale, Jul 06 2009 STATUS approved

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Last modified December 5 01:43 EST 2022. Contains 358572 sequences. (Running on oeis4.)