cp's OEIS Frontend

A273844 Least number k such that j*Sd(k) = Sd(k^j) for 1 <= j <= n, where Sd(k) is the sum of the digits of k.

%I A273844 #12 Jun 12 2016 13:14:15
%S A273844 1,2,27,36,405,11682,33651,669024,25274655,40809168,59716233,
%T A273844 7932651138,367732181646
%N A273844 Least number k such that j*Sd(k) = Sd(k^j) for 1 <= j <= n, where Sd(k) is the sum of the digits of k.
%C A273844 a(14) > 10^12. - _Giovanni Resta_, Jun 02 2016
%e A273844 For n=2, 2*Sd(2) = 2*2 = 4 and Sd(2^2) = Sd(4) = 4.
%e A273844 For n=3, 2*Sd(27) = 2*9 = 18 and Sd(27^2) = Sd(729) = 18;
%e A273844      and 3*Sd(27) = 3*9 = 27 and Sd(27^3) = Sd(19683) = 27.
%p A273844 T:=proc(w) local x, y, z; x:=w; y:=0; for z from 1 to ilog10(x)+1 do
%p A273844 y:=y+(x mod 10); x:=trunc(x/10); od; y; end:
%p A273844 P:=proc(q) local a,j,k,n,ok,t; t:=1; for k from 1 to q do
%p A273844 for n from t to q do ok:=1; a:=T(n);
%p A273844 for j from 2 to k do if j*a<>T(n^j) then ok:=0; break; fi; od;
%p A273844 if ok=1 then t:=n; print(n); break; fi; od; od; end: P(10^20);
%Y A273844 Cf. A007953, A124359.
%K A273844 nonn,base,more
%O A273844 1,2
%A A273844 _Paolo P. Lava_, Jun 01 2016
%E A273844 a(12)-a(13) from _Giovanni Resta_, Jun 02 2016