

A305800


Filter sequence for a(prime) = constant sequences.


22



1, 2, 2, 3, 2, 4, 2, 5, 6, 7, 2, 8, 2, 9, 10, 11, 2, 12, 2, 13, 14, 15, 2, 16, 17, 18, 19, 20, 2, 21, 2, 22, 23, 24, 25, 26, 2, 27, 28, 29, 2, 30, 2, 31, 32, 33, 2, 34, 35, 36, 37, 38, 2, 39, 40, 41, 42, 43, 2, 44, 2, 45, 46, 47, 48, 49, 2, 50, 51, 52, 2, 53, 2, 54, 55, 56, 57, 58, 2, 59, 60, 61, 2, 62, 63, 64, 65, 66, 2, 67, 68, 69, 70, 71, 72, 73, 2, 74, 75, 76, 2, 77, 2, 78, 79, 80, 2, 81, 2, 82, 83, 84, 2, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96
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OFFSET

1,2


COMMENTS

Restricted growth sequence transform of A239968.
In the following, A stands for this sequence, A305800, and S > T (where S and T are sequence Anumbers) indicates that for all i, j: S(i) = S(i) => T(i) = T(j).
For example, the following implications hold:
A > A300247 > A305897 > A077462 > A101296,
A > A290110 > A300250 > A101296.


LINKS

Antti Karttunen, Table of n, a(n) for n = 1..100000


FORMULA

a(1) = 1; for n > 1, a(n) = 2 for prime n, and a(n) = 1+nA000720(n) for composite n.


MATHEMATICA

Join[{1}, Table[If[PrimeQ[n], 2, 1+nPrimePi[n]], {n, 2, 150}]] (* Harvey P. Dale, Jul 12 2019 *)


PROG

(PARI) A305800(n) = if(1==n, n, if(isprime(n), 2, 1+nprimepi(n)));


CROSSREFS

Cf. A000720, A239968.
Differs from A296073 for the first time at n=125, as a(125) = 96, while A296073(125) = 33.
Cf. also A305900, A305801, A295300, A289626 for other "upper level" filters.
Sequence in context: A319693 A296073 A317943 * A293442 A318470 A175501
Adjacent sequences: A305797 A305798 A305799 * A305801 A305802 A305803


KEYWORD

nonn


AUTHOR

Antti Karttunen, Jun 14 2018


STATUS

approved



