A282764 9*n analog to Keith numbers.

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

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