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A282764
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9*n analog to Keith numbers.
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2
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9, 17, 48, 55, 96, 120, 124, 131, 244, 426, 787, 1893, 5307, 5364, 5600, 10083, 31085, 46733, 52700, 53456, 56857, 56920, 109620, 110313, 110376, 374016, 2989245, 4081505, 5173765, 13017112, 17242512, 34346372, 34638676
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OFFSET
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1,1
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COMMENTS
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Like Keith numbers but starting from 9*n digits to reach n.
Consider the digits of 9*n. Take their sum and repeat the process deleting the first addend and adding the previous sum. The sequence lists the numbers that after some iterations reach a sum equal to themselves.
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LINKS
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Table of n, a(n) for n=1..33.
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EXAMPLE
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9*17 = 153:
1 + 5 + 3 = 9;
5 + 3 + 9 = 17.
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MAPLE
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with(numtheory): P:=proc(q, h, w) local a, b, k, n, t, v; v:=array(1..h);
for n from 1 to q do a:=w*n; b:=ilog10(a)+1; if b>1 then
for k from 1 to b do v[b-k+1]:=(a mod 10); a:=trunc(a/10); od; t:=b+1; v[t]:=add(v[k], k=1..b); while v[t]<n do t:=t+1; v[t]:=add(v[k], k=t-b..t-1); od;
if v[t]=n then print(n); fi; fi; od; end: P(10^6, 1000, 9);
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MATHEMATICA
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Select[Range[10^6], Function[n, Module[{d = IntegerDigits[9 n], s, k = 0}, s = Total@ d; While[s < n, AppendTo[d, s]; k++; s = 2 s - d[[k]]]; s == n]]] (* Michael De Vlieger, Feb 22 2017, after T. D. Noe at A007629 *)
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CROSSREFS
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Cf. A282757 - A282763, A282765.
Sequence in context: A318755 A146576 A147138 * A319018 A101304 A146601
Adjacent sequences: A282761 A282762 A282763 * A282765 A282766 A282767
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KEYWORD
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nonn,base
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AUTHOR
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Paolo P. Lava, Feb 22 2017
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STATUS
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approved
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