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 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 (list; graph; refs; listen; history; text; internal format)
 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 * A293442 A318470 A175501 Adjacent sequences:  A305797 A305798 A305799 * A305801 A305802 A305803 KEYWORD nonn AUTHOR Antti Karttunen, Jun 14 2018 STATUS approved

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Last modified September 16 02:16 EDT 2019. Contains 327088 sequences. (Running on oeis4.)