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A282764 9*n analog to Keith numbers. 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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.

LINKS

Table of n, a(n) for n=1..33.

EXAMPLE

9*17 = 153:

1 + 5 + 3 = 9;

5 + 3 + 9 = 17.

MAPLE

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);

MATHEMATICA

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 *)

CROSSREFS

Cf. A282757 - A282763, A282765.

Sequence in context: A318755 A146576 A147138 * A319018 A101304 A146601

Adjacent sequences:  A282761 A282762 A282763 * A282765 A282766 A282767

KEYWORD

nonn,base

AUTHOR

Paolo P. Lava, Feb 22 2017

STATUS

approved

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Last modified August 20 22:45 EDT 2019. Contains 326155 sequences. (Running on oeis4.)