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A377416 Least integer k which, by a process analogous to the Keith numbers, reach k + n.

%I A377416 #13 Sep 01 2025 18:34:25
%S A377416 14,12,11,10,16,13,17,37,18,12,11,10,40,15,27,39,13,16,24,67,22,17,12,
%T A377416 11,10,18,21,36,43,19,15,58,23,30,13,51,48,16,54,27,44,38,34,12,11,10,
%U A377416 14,91,20,32,55,18,42,29,35,21,25,277,15,150,66,72,56,13,46
%N A377416 Least integer k which, by a process analogous to the Keith numbers, reach k + n.
%H A377416 Paolo P. Lava, <a href="/A377416/b377416.txt">Table of n, a(n) for n = 0..1000</a>
%e A377416 a(5) = 13 because 1 + 3 = 4, 3 + 4 = 7, 4 + 7 = 11, 7 + 11 = 18 that is 13 + 5.
%p A377416 with(numtheory): P:=proc(q,h) local a,b,c,j,k,n,t,v; v:=array(1..h); c:=[];
%p A377416 for j from 0 to 59 do for n from 10 to q do a:=n; b:=length(a);
%p A377416 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 A377416 while v[t]<n+j do t:=t+1; v[t]:=add(v[k],k=t-b..t-1); od; if v[t]=n+j then c:=[op(c),n]; break;
%p A377416 fi; od; od; op(c); end: P(10^6,5000);
%Y A377416 Cf. A007629, A377439.
%K A377416 nonn,easy,base,changed
%O A377416 0,1
%A A377416 _Paolo P. Lava_, Oct 27 2024