A281915 4th power analog of Keith numbers.

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

Offset: 1

Author

Paolo P. Lava, Feb 02 2017

Keywords

• nonn
• base

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.

Examples

			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.
		

Crossrefs

Cf. A055575, A007629, A246544, A263534.

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

Programs

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]
				

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 *)

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