A366833 Number of times n appears in A362965 (number of primes <= the n-th prime power).

1, 2, 1, 3, 1, 2, 1, 1, 3, 1, 2, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 3, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1

Offset

1,2

Comments

Conjecture: a(n) can be only 1, 2, or 3 (with the first occurrences of 3 appearing at n = 4, 9, 30, 327 and 3512).

Links

Paolo Xausa, Table of n, a(n) for n = 1..10000

Paolo Xausa, 1200 X 1200 raster image of a(n), n = 1..1440000, read left to right, top to bottom, showing a(n) = 1 in blue, a(n) = 2 in white and a(n) = 3 in red.

Mathematica

With[{upto=1000}, Map[Length, Most[Split[PrimePi[Select[Range[upto], PrimePowerQ]]]]]] (* Considers prime powers up to 1000 *)

Crossrefs

Run lengths of A362965.

Cf. A068435, A075526, A246655, A366835.

Sequence in context: A092782 A119647 A228098 * A353161 A327533 A327518

Adjacent sequences: A366830 A366831 A366832 * A366834 A366835 A366836

Keyword

nonn

Author

Paolo Xausa, Oct 25 2023

Status

approved