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n/7 analog of Keith numbers.
4

%I #14 Mar 07 2017 20:58:06

%S 301,602,1113,4942,478205,23942940,47885880,178114489749

%N n/7 analog of Keith numbers.

%C Like Keith numbers but starting from n/7 digits to reach n.

%C Consider the digits of n/7. 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.

%C If it exists, a(9) > 10^12. - _Lars Blomberg_ Mar 07 2017

%e 1113/7 = 159:

%e 1 + 5 + 9 = 15;

%e 5 + 9 + 15 = 29;

%e 9 + 15 + 29 = 53;

%e 15 + 29 + 53 = 97;

%e 29 + 53 + 97 = 179;

%e 53 + 97 + 179 = 329;

%e 97 + 179 + 329 = 605;

%e 179 + 329 + 605 = 1113.

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

%p for n from 1/w by 1/w 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);

%p 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, 1000,1/7);

%t With[{n = 7}, Select[Range[10 n, 10^6, n], Function[k, Last@ NestWhile[Append[Rest@ #, Total@ #] &, IntegerDigits[k/n], Total@ # <= k &] == k]]] (* _Michael De Vlieger_, Feb 27 2017 *)

%Y Cf. A282757 - A282765, A282766 - A282768.

%K nonn,base,more

%O 1,1

%A _Paolo P. Lava_, Feb 27 2017

%E a(8) from _Lars Blomberg_, Mar 07 2017