%I #6 Feb 23 2017 22:53:58
%S 7,9,14,19,21,28,38,53,54,76,92,124,1299,18185,20468,31871,32054,
%T 37903,128200,152057,175539,193399,214631,303677,1806425,3250457,
%U 3616693,7870170,10793441,12047403,13781464,15035426,18663611,19917573,22905596,46531972,101743590
%N 3*n analog to Keith numbers.
%C Like Keith numbers but starting from 3*n digits to reach n.
%C Consider the digits of 3*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 3*28 = 84:
%e 8 + 4 = 12;
%e 4 + 12 = 16;
%e 12 + 16 = 28.
%p with(numtheory): P:=proc(q, h,w) local a, b, k, n, t, v; v:=array(1..h);
%p for n from 1 to q do a:=w*n; b:=ilog10(a)+1; if b>1 then
%p for k from 1 to b do v[b-k+1]:=(a mod 10); a:=trunc(a/10); od; t:=b+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;
%p if v[t]=n then print(n); fi; fi; od; end: P(10^6, 1000,3);
%t Select[Range[10^6], Function[n, Module[{d = IntegerDigits[3 n], 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 *)
%Y Cf. A282757, A282759 - A282765.
%K nonn,base
%O 1,1
%A _Paolo P. Lava_, Feb 22 2017