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 A305979 Filter sequence for a(Fermi-Dirac primes) = constant sequences. 4
 1, 2, 2, 2, 2, 3, 2, 4, 2, 5, 2, 6, 2, 7, 8, 2, 2, 9, 2, 10, 11, 12, 2, 13, 2, 14, 15, 16, 2, 17, 2, 18, 19, 20, 21, 22, 2, 23, 24, 25, 2, 26, 2, 27, 28, 29, 2, 30, 2, 31, 32, 33, 2, 34, 35, 36, 37, 38, 2, 39, 2, 40, 41, 42, 43, 44, 2, 45, 46, 47, 2, 48, 2, 49, 50, 51, 52, 53, 2, 54, 2, 55, 2, 56, 57, 58, 59, 60, 2, 61, 62, 63, 64, 65, 66, 67, 2, 68, 69, 70, 2 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS For all i, j: a(i) = a(j) => A305976(i) = A305976(j). a(i) = a(j) => A302791(i) = A302791(j). LINKS Antti Karttunen, Table of n, a(n) for n = 1..100000 FORMULA a(1) = 1; for n > 1, if A302777(n) is 1 [when n is in A050376], a(n) = 2, otherwise a(n) = 1 + n - A302778(n) = running count from 3 onward. PROG (PARI) up_to = 100000; partialsums(f, up_to) = { my(v = vector(up_to), s=0); for(i=1, up_to, s += f(i); v[i] = s); (v); } A209229(n) = (n && !bitand(n, n-1)); A302777(n) = A209229(isprimepower(n)); v302778 = partialsums(A302777, up_to); A302778(n) = v302778[n]; A305979(n) = if(1==n, n, if(1==A302777(n), 2, 1+n-A302778(n))); CROSSREFS Cf. A050376, A302777, A302778, A302791, A305975, A305976. Sequence in context: A293444 A302791 A334868 * A366805 A293223 A361514 Adjacent sequences: A305976 A305977 A305978 * A305980 A305981 A305982 KEYWORD nonn AUTHOR Antti Karttunen, Jul 02 2018 STATUS approved

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Last modified May 18 18:37 EDT 2024. Contains 372664 sequences. (Running on oeis4.)