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A171785
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Start with a(1) = 1; then a(n) = smallest number > a(n-1) such that a(n) divides concat(a(1), a(2), ..., a(n)).
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10
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1, 2, 3, 5, 10, 12, 15, 20, 25, 30, 39, 44, 50, 100, 101, 125, 150, 188, 200, 220, 230, 250, 272, 304, 320, 370, 376, 400, 500, 525, 600, 615, 625, 1000, 1250, 1487, 1500, 1590, 1696, 1750, 2000, 2245, 2500, 3000, 3090, 3125, 3800, 4000, 5000, 5725, 6122, 7025
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OFFSET
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1,2
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COMMENTS
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Primes appearing so far are 2, 3, 5, 101, 1487.
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LINKS
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R. G. Wilson v, Table of n, a(n) for n = 1..584
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EXAMPLE
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1: 1 divides 1
1,2: 2 divides 12
1,2,3: 3 divides 123
1,2,3,4: 4 does NOT divide 1234, so
1,2,3,5: 5 divides 1235
etc.
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MAPLE
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with(numtheory); P:=proc(q) local a, n; a:=0;
for n from 1 to q do if type((a*10^(1+ilog10(n))+n)/n, integer)
then a:=a*10^(1+ilog10(n))+n; print(n); fi; od; end: P(10^5); # Paolo P. Lava, Nov 27 2014
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MATHEMATICA
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f[s_List] := Block[{k = s[[ -1]] + 1, conc = FromDigits[Flatten@ IntegerDigits@s]}, While[ Mod[conc*10^Floor[ Log[10, k] + 1] + k, k] != 0, k++ ]; Append[s, k]]; Nest[f, {1}, 51] (* Robert G. Wilson v, Oct 14 2010 *)
nxt[{a_, c_}]:=Module[{k=a+1}, While[!Divisible[c*10^IntegerLength[k]+ k, k], k++]; {k, c*10^IntegerLength[k]+k}]; Transpose[NestList[nxt, {1, 1}, 60]][[1]] (* Harvey P. Dale, Mar 08 2015 *)
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CROSSREFS
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See A029455 for numbers that divide the concatenation of all numbers <= n.
Sequence in context: A039022 A182402 A079251 * A050051 A252353 A241167
Adjacent sequences: A171782 A171783 A171784 * A171786 A171787 A171788
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KEYWORD
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nonn,base
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AUTHOR
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David Scambler, Sep 30 2010
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EXTENSIONS
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More terms from Robert G. Wilson v, Oct 14 2010
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STATUS
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approved
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