A274770 Cube analog to Keith numbers.

1, 8, 17, 18, 26, 27, 44, 55, 63, 80, 105, 187, 326, 776, 1095, 2196, 6338, 13031, 13131, 25562, 27223, 70825, 140791, 553076, 632489, 1402680, 1404312, 3183253, 11311424, 50783292, 51231313, 182252596, 255246098, 522599548, 1180697763, 2025114819, 2137581414

Offset

1,2

Comments

Like Keith numbers but starting from n^3 digits to reach n.

Consider the digits of the cube of a number 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..37.

Example

776^3 = 467288576 :
4 + 6 + 7 + 2 + 8 + 8 + 5 + 7 + 6 = 53;
6 + 7 + 2 + 8 + 8 + 5 + 7 + 6 + 53 = 102;
7 + 2 + 8 + 8 + 5 + 7 + 6 + 53 + 102 = 198;
2 + 8 + 8 + 5 + 7 + 6 + 53 + 102 + 198 = 389;
8 + 8 + 5 + 7 + 6 + 53 + 102 + 198 + 389 = 776.

Maple

with(numtheory): P:=proc(q, h) local a, b, k, n, t, v; v:=array(1..h);
for n from 1 to q do b:=n^3; a:=[];
for k from 1 to ilog10(b)+1 do a:=[(b mod 10), op(a)]; b:=trunc(b/10); od;
for k from 1 to nops(a) do v[k]:=a[k]; od; b:=ilog10(n^3)+1;
t:=nops(a)+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; od; end: P(10^6, 10000);

Mathematica

(* function keithQ[ ] is defined in A007629 *)
a274770[n_] := Join[{1, 8}, Select[Range[10, n], keithQ[#, 3]&]]
a274770[10^6] (* Hartmut F. W. Hoft, Jun 02 2021 *)

Crossrefs

Cf. A007629, A246544, A263534, A274769.

Sequence in context: A302976 A244537 A046459 * A075485 A217433 A271626

Adjacent sequences: A274767 A274768 A274769 * A274771 A274772 A274773

Keyword

nonn,base

Author

Paolo P. Lava, Jul 06 2016

Extensions

a(34)-a(37) from Giovanni Resta, Jul 08 2016

Status

approved