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

Author

Antti Karttunen, Jun 14 2018

Keywords

• nonn

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

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.

Programs

Mathematica

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

PARI

A305800(n) = if(1==n,n,if(isprime(n),2,1+n-primepi(n)));

Formula

a(1) = 1; for n > 1, a(n) = 2 for prime n, and a(n) = 1+n-A000720(n) for composite n.