A282759 4*n analog to Keith numbers.

3, 6, 9, 12, 19, 29, 40, 787, 1679, 2137, 2508, 2728, 5016, 7524, 12773, 36183, 46116, 192952, 246916, 681538, 1316065, 4826672, 7571204, 8709926, 9716827, 24922317

Offset

1,1

Comments

Like Keith numbers but starting from 4*n digits to reach n.

Consider the digits of 4*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..26.

Example

4*29 = 116:
1 + 1 + 6 = 8;
1 + 6 + 8 = 15;
6 + 8 + 15 = 29.

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, 4);

Mathematica

Select[Range[10^6], Function[n, Module[{d = IntegerDigits[4 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 *)

Crossrefs

Cf. A282757, A282758, A282760 - A282765.

Sequence in context: A109657 A175589 A348339 * A203016 A153838 A143829

Adjacent sequences: A282756 A282757 A282758 * A282760 A282761 A282762

Keyword

nonn,base

Author

Paolo P. Lava, Feb 22 2017

Status

approved