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A281915 4th power analog of Keith numbers. 9
1, 7, 19, 20, 22, 25, 28, 36, 77, 107, 110, 175, 789, 1528, 1932, 3778, 5200, 7043, 8077, 38855, 41234, 44884, 49468, 204386, 763283, 9423515, 73628992, 87146144, 146124072, 146293356, 326194628, 1262293219, 1321594778, 2767787511, 11511913540, 12481298961, 13639550655 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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

Consider the digits of n^4. 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

Table of n, a(n) for n=1..37.

EXAMPLE

175^4 = 937890625:

9 + 3 + 7 + 8 + 9 + 0 + 6 + 2 + 5 = 49;

3 + 7 + 8 + 9 + 0 + 6 + 2 + 5 + 49 = 89;

7 + 8 + 9 + 0 + 6 + 2 + 5 + 49 + 89 = 175.

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 *)

a281915[n_] := Join[{1, 7}, Select[Range[10, n], keithQ[#, 4]&]]

a281915[10^6] (* Hartmut F. W. Hoft, Jun 02 2021 *)

CROSSREFS

Cf. A055575, A007629, A246544, A263534.

Cf. A274769, A274770, A281916, A281917, A281918, A281919, A281920, A281921.

Sequence in context: A344711 A052256 A064819 * A102167 A214525 A109637

Adjacent sequences:  A281912 A281913 A281914 * A281916 A281917 A281918

KEYWORD

nonn,base

AUTHOR

Paolo P. Lava, Feb 02 2017

EXTENSIONS

a(27)-a(28) from Jinyuan Wang, Jan 30 2020

Missing a(25) and a(29)-a(37) from Giovanni Resta, Jan 31 2020

STATUS

approved

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Last modified January 19 20:48 EST 2022. Contains 350466 sequences. (Running on oeis4.)