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A375119 Begin A060403 with n instead of 1; a(n) is the position in the new sequence at which it generates the same numbers as A060403 or a(n)=0 if it doesn't.

%I A375119 #14 Apr 26 2025 20:12:11
%S A375119 1,4,2,1,3,3,6,1,2,2,5,5,1,5,5,6,4,4,10,4,1,4,5,5,3,3,9,9,9,1,3,9,4,4,
%T A375119 2,1,8,8,8,2,8,5,3,3,1,2,27,7,7,4,7,5,2,1,3,3,26,6,6,4,6,26,1,2,3,3,
%U A375119 25,5,5,25,5,25,1,2,3,3,24,4,4,3,4,24,113
%N A375119 Begin A060403 with n instead of 1; a(n) is the position in the new sequence at which it generates the same numbers as A060403 or a(n)=0 if it doesn't.
%C A375119 The indices of the matching entries of A060403 and this sequence do not necessarily have to be the same (see Examples).
%H A375119 James C. McMahon, <a href="/A375119/b375119.txt">Table of n, a(n) for n = 1..1000</a>
%H A375119 Wikipedia,<a href="https://en.wikipedia.org/wiki/Kruskal_count">Kruskal count</a>
%e A375119 Using () to indicate the point at which the new sequence generates the same numbers as A060403:
%e A375119   A060403: 1, 4, 8, 13, 21, 30, 36, 45...      a(1)=1
%e A375119   Start=2: 2, 6, 9, (13), 21, 30, 36, 45...    a(2)=4
%e A375119   Start=3: 3, (8), 13, 21, 30, 36, 45...       a(3)=2
%e A375119   Start=4: (4), 8, 13, 21, 30, 36, 45...       a(4)=1
%t A375119 oneseq=NestList[#+Length[Select[Characters[IntegerName[#,"Words"]],LetterQ ]]&,1,200] (* oneseq is A060403 *);seq={};Do[ i=1;s=n;While[!MemberQ[oneseq,s],s=s+Length[Select[Characters[IntegerName[s,"Words"]],LetterQ ]];i++];AppendTo[seq,i],{n,83}];seq
%Y A375119 Cf. A060403.
%K A375119 nonn,base
%O A375119 1,2
%A A375119 _James C. McMahon_, Jul 30 2024