A274769 - OEIS

%I #22 Jun 02 2021 22:22:34

%S 1,9,37,40,43,62,70,74,160,1264,1952,2847,12799,16368,16584,42696,

%T 83793,97415,182011,352401,889871,925356,1868971,1881643,3661621,

%U 7645852,15033350,21655382,63288912,88192007,158924174,381693521,792090500,2025078249,2539401141

%N Square analog to Keith numbers.

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

%C 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.

%e 1264^2 = 1597696 :

%e 1 + 5 + 9 + 7 + 6 + 9 + 6 = 43;

%e 5 + 9 + 7 + 6 + 9 + 6 + 43 = 85;

%e 9 + 7 + 6 + 9 + 6 + 43 + 85 = 165;

%e 7 + 6 + 9 + 6 + 43 + 85 + 165 = 321;

%e 6 + 9 + 6 + 43 + 85 + 165 + 321 = 635;

%e 9 + 6 + 43 + 85 + 165 + 321 + 635 = 1264.

%p with(numtheory): P:=proc(q, h) local a,b,k,n,t,v; v:=array(1..h);

%p for n from 1 to q do b:=n^2; a:=[];

%p for k from 1 to ilog10(b)+1 do a:=[(b mod 10),op(a)]; b:=trunc(b/10); od;

%p for k from 1 to nops(a) do v[k]:=a[k]; od; b:=ilog10(n^2)+1;

%p 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);

%p od; if v[t]=n then print(n); fi; od; end: P(10^6, 10000);

%t 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 *)

%t (* function keithQ[ ] is defined in A007629 *)

%t a274769[n_] := Join[{1, 9}, Select[Range[10, n], keithQ[#, 2]&]]

%t a274769[10^6] (* _Hartmut F. W. Hoft_, Jun 02 2021 *)

%Y Cf. A007629, A246544, A263534, A274770.

%K nonn,base

%O 1,2

%A _Paolo P. Lava_, Jul 06 2016

%E a(32)-a(35) from _Giovanni Resta_, Jul 08 2016