A282762 7*n analog to Keith numbers.

3, 6, 9, 12, 25, 29, 33, 58, 62, 66, 70, 87, 91, 95, 99, 124, 128, 150, 152, 165, 178, 191, 204, 217, 592, 801, 1184, 3860, 15728, 59800, 117711, 157701, 230720, 270737, 496085, 795918, 869366, 954639, 1549319, 1826773, 3169440, 3170466, 3973793, 3974819, 3975845, 4012718, 4013744, 5120160, 5653357, 5978943

Offset

1,1

Comments

Like Keith numbers but starting from 7*n digits to reach n.

Consider the digits of 7*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..50.

Example

7*25 = 175:
1 + 7 + 5 = 13;
7 + 5 + 13 =25.

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, 7);

Mathematica

Select[Range[10^6], Function[n, Module[{d = IntegerDigits[7 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 - A282761, A282763 - A282765.

Sequence in context: A277823 A233155 A118519 * A089757 A294569 A277250

Adjacent sequences: A282759 A282760 A282761 * A282763 A282764 A282765

Keyword

nonn,base

Author

Paolo P. Lava, Feb 22 2017

Status

approved