A274769 Square analog to Keith numbers.

1, 9, 37, 40, 43, 62, 70, 74, 160, 1264, 1952, 2847, 12799, 16368, 16584, 42696, 83793, 97415, 182011, 352401, 889871, 925356, 1868971, 1881643, 3661621, 7645852, 15033350, 21655382, 63288912, 88192007, 158924174, 381693521, 792090500, 2025078249, 2539401141

Offset

1,2

Comments

Like Keith numbers but starting from n^2 digits to reach n.

Consider the digits of the square 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.

Links

Table of n, a(n) for n=1..35.

Example

1264^2 = 1597696 :
1 + 5 + 9 + 7 + 6 + 9 + 6 = 43;
5 + 9 + 7 + 6 + 9 + 6 + 43 = 85;
9 + 7 + 6 + 9 + 6 + 43 + 85 = 165;
7 + 6 + 9 + 6 + 43 + 85 + 165 = 321;
6 + 9 + 6 + 43 + 85 + 165 + 321 = 635;
9 + 6 + 43 + 85 + 165 + 321 + 635 = 1264.

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^2; 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^2)+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

Select[Range[10^6], Function[n, Module[{d = IntegerDigits[n^2], s, k = 0}, s = Total@ d; While[s < n, AppendTo[d, s]; k++; s = 2 s - d[[k]]]; s == n]]] (* Michael De Vlieger, Feb 22 2017, after T. D. Noe at A007629 *)
(* function keithQ[ ] is defined in A007629 *)
a274769[n_] := Join[{1, 9}, Select[Range[10, n], keithQ[#, 2]&]]
a274769[10^6] (* Hartmut F. W. Hoft, Jun 02 2021 *)

Crossrefs

Cf. A007629, A246544, A263534, A274770.

Sequence in context: A232257 A091961 A103758 * A126914 A337238 A273594

Adjacent sequences: A274766 A274767 A274768 * A274770 A274771 A274772

Keyword

nonn,base

Author

Paolo P. Lava, Jul 06 2016

Extensions

a(32)-a(35) from Giovanni Resta, Jul 08 2016

Status

approved