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.

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

Offset: 1

Author

James C. McMahon, Aug 18 2024

Keywords

• nonn

Comments

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

Examples

			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
		

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

Crossrefs

Cf. A160649.

Programs

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 *)