A305800 Filter sequence for a(prime) = constant sequences.

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

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 A-numbers) 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+n-A000720(n) for composite n.

Mathematica

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

Prog

(PARI) A305800(n) = if(1==n, n, if(isprime(n), 2, 1+n-primepi(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 * A366293 A293442 A318470

Adjacent sequences: A305797 A305798 A305799 * A305801 A305802 A305803

Keyword

nonn

Author

Antti Karttunen, Jun 14 2018

Status

approved