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

1,4

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 A375510 A375511

Keyword

nonn

Author

James C. McMahon, Aug 18 2024

Status

approved