A281918 7th power analog of Keith numbers.

1, 18, 27, 31, 34, 43, 53, 58, 68, 145, 187, 314, 826, 2975, 37164, 40853, 58530, 72795, 77058, 160703, 187617, 1926759, 6291322, 6628695, 25285305, 31292514, 33968486, 54954185, 71593237, 125921697, 555963577, 575307142, 2393596216, 2444508547, 42544333760, 97812197525

Offset

1,2

Comments

Like Keith numbers but starting from n^7 digits to reach n.

Consider the digits of n^7. 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.

a(30) > 10^8. - Jinyuan Wang, Jan 30 2020

Links

Table of n, a(n) for n=1..36.

Example

145^7 = 1347646586640625:
1 + 3 + 4 + 7 + 6 + 4 + 6 + 5 + 8 + 6 + 6 + 4 + 0 + 6 + 2 + 5 = 73;
3 + 4 + 7 + 6 + 4 + 6 + 5 + 8 + 6 + 6 + 4 + 0 + 6 + 2 + 5 + 73 = 145.

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, 7);

Mathematica

(* function keithQ[ ] is defined in A007629 *)
a281918[n_] := Join[{1}, Select[Range[10, n], keithQ[#, 7]&]]
a281918[10^6] (* Hartmut F. W. Hoft, Jun 03 2021 *)

Crossrefs

Cf. A226971, A007629, A246544, A263534.

Cf. A274769, A274770, A281915, A281916, A281917, A281919, A281920, A281921.

Sequence in context: A347826 A036763 A226971 * A186129 A284672 A265738

Adjacent sequences: A281915 A281916 A281917 * A281919 A281920 A281921

Keyword

nonn,base

Author

Paolo P. Lava, Feb 02 2017

Extensions

a(28)-a(29) from Jinyuan Wang, Jan 30 2020

a(30)-a(36) from Giovanni Resta, Feb 03 2020

Status

approved