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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.
1
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
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
KEYWORD
nonn
AUTHOR
James C. McMahon, Aug 18 2024
STATUS
approved