login
A305800
Filter sequence for a(prime) = constant sequences.
62
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
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
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
KEYWORD
nonn
AUTHOR
Antti Karttunen, Jun 14 2018
STATUS
approved