A375508 Contribution to the OEIS

 

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. 0

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, 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, 1, 4, 3, 1, 1, 4, 1, 2, 3, 1, 1, 2, 9, 9, 8, 1, 8, 1, 7 (list; graph; refs; listen; history; edit; text; internal format)

OFFSET 1,4 COMMENTS The indices of the matching entries of A160649 and this sequence do not necessarily have to be the same (see Examples). LINKS James C. McMahon, Table of n, a(n) for n = 1..10000 Michael De Vlieger, Histogram of the frequency of a(n) = k, n = 1..2^20, k = 1..14. Maximum in the dataset is k = 41. Michael De Vlieger, Histogram of the frequency of a(n) = k, n = 1..2^24, k = 1..14. Maximum in the dataset is k = 57. Wikipedia, Kruskal count EXAMPLE Using () to indicate the point at which the new sequence generates the same numbers as A160649: A160649: 2, 3, 4, 6, 8, 11, 12... a(1)=1 Start=3: (3), 4, 6, 8, 11, 12... a(2)=1 Start=4: (4), 6, 8, 11, 12, 15... a(3)=1 Start=5: 5, (6), 8, 11, 12, 15... a(4)=2 MATHEMATICA 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 *) CROSSREFS Cf. A160649. Sequence in context: A326194 A331251 A309858 * A022921 A080763 A245920 Adjacent sequences: A375505 A375506 A375507 * A375509 A375511 A375512 KEYWORD nonn,new AUTHOR James C. McMahon, Aug 18 2024 STATUS approved

Additional work on this sequence is given in the post: https://jamesmacmath.blogspot.com/2024/08/kruskal-count-with-prime-omega.html