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%I #14 Mar 13 2017 13:03:47
%S 45,609,1218,1827,3213,21309,28206,29319,31917,39333,47337,78666,
%T 102090,117999,204180,406437,302867592,4507146801,5440407522
%N n/3 analog of Keith numbers.
%C Like Keith numbers but starting from n/3 digits to reach n.
%C Consider the digits of n/3. 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(20) > 10^12. - _Lars Blomberg_ Mar 13 2017
%e 609/3 = 203:
%e 2 + 0 + 3 = 5;
%e 0 + 3 + 5 = 8;
%e 3 + 5 + 8 = 16;
%e 5 + 8 + 16 = 29;
%e 8 + 16 + 29 = 53;
%e 16 + 29 + 53 = 98;
%e 29 + 53 + 98 = 180;
%e 53 + 98 + 180 = 331;
%e 98 + 180 + 331 = 609.
%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, 1000,1/3);
%t With[{n = 3}, 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, A282769.
%K nonn,base,more
%O 1,1
%A _Paolo P. Lava_, Feb 27 2017
%E a(17)-a(19) from _Lars Blomberg_, Mar 13 2017
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