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A281919
8th-power analog of Keith numbers.
9
1, 30, 46, 54, 63, 207, 394, 693, 694, 718, 20196, 42664, 80051, 90135, 91447, 93136, 207846, 324121, 361401, 421609, 797607, 802702, 882227, 1531788, 1788757, 1789643, 4028916, 4176711, 6692664, 15643794, 31794346, 65335545, 140005632, 144311385, 153364253
OFFSET
1,2
COMMENTS
Like Keith numbers but starting from n^8 digits to reach n.
Consider the digits of n^8. Take their sum and repeat the process deleting the first addend and adding the previous sum. The sequence lists the numbers that after some number of iterations reach a sum equal to n.
LINKS
FORMULA
207^8 = 3371031134626313601:
3 + 3 + 7 + 1 + 0 + 3 + 1 + 1 + 3 + 4 + 6 + 2 + 6 + 3 + 1 + 3 + 6 + 0 + 1 = 54;
3 + 7 + 1 + 0 + 3 + 1 + 1 + 3 + 4 + 6 + 2 + 6 + 3 + 1 + 3 + 6 + 0 + 1 + 54 = 105;
7 + 1 + 0 + 3 + 1 + 1 + 3 + 4 + 6 + 2 + 6 + 3 + 1 + 3 + 6 + 0 + 1 + 54 + 105 = 207.
MAPLE
with(numtheory): P:=proc(q, h, w) local a, b, k, t, v; global n; v:=array(1..h);
for n from 1 to q do b:=n^w; 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^w)+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, 4);
MATHEMATICA
(* function keithQ[ ] is defined in A007629 *)
a281919[n_] := Join[{1}, Select[Range[10, n], keithQ[#, 8]&]]
a281919[10^6] (* Hartmut F. W. Hoft, Jun 03 2021 *)
KEYWORD
nonn,base
AUTHOR
Paolo P. Lava, Feb 02 2017
EXTENSIONS
a(32) from Jinyuan Wang, Feb 01 2020
Terms a(33) and beyond from Giovanni Resta, Feb 03 2020
STATUS
approved