A282763 - OEIS

%I #6 Feb 23 2017 22:54:28

%S 9,20,176,184,277,2669,15705,233202,241202,445657,742714,2095479,

%T 4697536,10508788,20308656,55683878,86603874

%N 8*n analog to Keith numbers.

%C Like Keith numbers but starting from 8*n digits to reach n.

%C Consider the digits of 8*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 8*20 = 160:

%e 1 + 6 + 0 = 7;

%e 6 + 0 + 7 = 13;

%e 0 + 7 + 13 = 20.

%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, 1000,8);

%t Select[Range[10^6], Function[n, Module[{d = IntegerDigits[8 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, after _T. D. Noe_ at A007629 *)

%Y Cf. A282757 - A282762, A282764, A282765.

%K nonn,base

%O 1,1

%A _Paolo P. Lava_, Feb 22 2017