A282759 - OEIS

%I #6 Feb 23 2017 22:54:04

%S 3,6,9,12,19,29,40,787,1679,2137,2508,2728,5016,7524,12773,36183,

%T 46116,192952,246916,681538,1316065,4826672,7571204,8709926,9716827,

%U 24922317

%N 4*n analog to Keith numbers.

%C Like Keith numbers but starting from 4*n digits to reach n.

%C Consider the digits of 4*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 4*29 = 116:

%e 1 + 1 + 6 = 8;

%e 1 + 6 + 8 = 15;

%e 6 + 8 + 15 = 29.

%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, 1000,4);

%t Select[Range[10^6], Function[n, Module[{d = IntegerDigits[4 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, A282758, A282760 - A282765.

%K nonn,base

%O 1,1

%A _Paolo P. Lava_, Feb 22 2017