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A375508 Begin A160649 with n instead of 2; a(n) is the position in the new sequence at which it generates the same numbers as A160649 or a(n)=0 if it doesn't.

%I A375508 #17 Sep 13 2024 07:31:22
%S A375508 1,1,1,2,1,2,1,2,2,1,1,5,4,1,3,1,1,3,2,1,2,1,1,6,2,5,1,5,4,1,1,3,3,2,
%T A375508 2,1,1,5,1,4,3,2,1,2,2,1,1,3,2,2,5,1,1,4,2,3,1,2,1,3,2,7,1,7,6,6,5,5,
%U A375508 1,4,3,1,1,4,1,2,3,1,1,2,9,9,8,1,8,1,7
%N A375508 Begin A160649 with n instead of 2; a(n) is the position in the new sequence at which it generates the same numbers as A160649 or a(n)=0 if it doesn't.
%C A375508 The indices of the matching entries of A160649 and this sequence do not necessarily have to be the same (see Examples).
%H A375508 James C. McMahon, <a href="/A375508/b375508.txt">Table of n, a(n) for n = 1..10000</a>
%H A375508 Michael De Vlieger, <a href="/A375508/a375508.png">Histogram of the frequency of a(n) = k</a>, n = 1..2^20, k = 1..14. Maximum in the dataset is k = 41.
%H A375508 Michael De Vlieger, <a href="/A375508/a375508_1.png">Histogram of the frequency of a(n) = k</a>, n = 1..2^24, k = 1..14. Maximum in the dataset is k = 57.
%H A375508 Wikipedia, <a href="https://en.wikipedia.org/wiki/Kruskal_count">Kruskal count</a>
%e A375508 Using () to indicate the point at which the new sequence generates the same numbers as A160649:
%e A375508 A160649: 2, 3, 4, 6, 8, 11, 12...  a(1)=1
%e A375508 Start=3: (3), 4, 6, 8, 11, 12...   a(2)=1
%e A375508 Start=4: (4), 6, 8, 11, 12, 15...  a(3)=1
%e A375508 Start=5: 5, (6), 8, 11, 12, 15...  a(4)=2
%t A375508 Lim=88;pseq1=NestList[#+PrimeOmega[#]&,2,Lim] (* pseq1 is base sequence A160649 *); pseq={}; Do[ i=1; s=n; While[!MemberQ[pseq1, s], s=s+PrimeOmega[s]; i++]; AppendTo[pseq, i], {n,2, Lim}];pseq (* pseq is A375508 *)
%Y A375508 Cf. A160649.
%K A375508 nonn
%O A375508 1,4
%A A375508 _James C. McMahon_, Aug 18 2024