A375508 - OEIS

%I #17 Sep 13 2024 07:31:22

%S 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 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 1,4,3,1,1,4,1,2,3,1,1,2,9,9,8,1,8,1,7

%N 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 The indices of the matching entries of A160649 and this sequence do not necessarily have to be the same (see Examples).

%H James C. McMahon, <a href="/A375508/b375508.txt">Table of n, a(n) for n = 1..10000</a>

%H 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 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 Wikipedia, <a href="https://en.wikipedia.org/wiki/Kruskal_count">Kruskal count</a>

%e Using () to indicate the point at which the new sequence generates the same numbers as A160649:

%e A160649: 2, 3, 4, 6, 8, 11, 12...  a(1)=1

%e Start=3: (3), 4, 6, 8, 11, 12...   a(2)=1

%e Start=4: (4), 6, 8, 11, 12, 15...  a(3)=1

%e Start=5: 5, (6), 8, 11, 12, 15...  a(4)=2

%t 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 Cf. A160649.

%K nonn

%O 1,4

%A _James C. McMahon_, Aug 18 2024