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A274770
Cube analog to Keith numbers.
11
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.
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
KEYWORD
nonn,base
AUTHOR
Paolo P. Lava, Jul 06 2016
EXTENSIONS
a(34)-a(37) from Giovanni Resta, Jul 08 2016
STATUS
approved