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 A294602 a(n) = pi(n-1) - pi(floor(n/2)), where pi is A000720. 2
 0, 0, 1, 1, 1, 1, 1, 2, 2, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 4, 4, 3, 3, 4, 4, 3, 3, 3, 3, 4, 4, 5, 5, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 6, 6, 5, 5, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 10, 10, 9, 9, 10, 10, 9 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,8 COMMENTS Number of primes in the interval (n/2, n). Number of primes among the larger parts of the partitions of n into two distinct parts. For n=8, the partitions of 8 into two distinct parts are (7,1), (6,2), (5,3); 7 and 5 are prime so a(8) = 2. - Wesley Ivan Hurt, Apr 07 2018 LINKS FORMULA a(n) = A056171(n) - A010051(n). a(n) = Sum_{i=1..floor((n-1)/2)} A010051(n-i). - Wesley Ivan Hurt, Apr 07 2018 EXAMPLE a(8) = 2 because there are 2 primes between 4 and 8: 5, 7. a(19) = 3 because there are 3 primes between 9 and 19: 11, 13, 17. MAPLE A294602 := proc(n)     numtheory[pi](n-1)-numtheory[pi](floor(n/2)) ; end proc: seq(A294602(n), n=1..120) ; # R. J. Mathar, Dec 17 2017 MATHEMATICA Array[PrimePi[# - 1] - PrimePi[Floor[#/2]] &, 86] (* Michael De Vlieger, Nov 03 2017 *) PROG (MAGMA) [0, 0] cat [#PrimesInInterval(Floor(n/2)+1, n-1): n in [3..86]]; (PARI) vector(86, n, primepi(n-1)-primepi(n\2)) CROSSREFS Cf. A000720, A001221, A010051, A056171. Sequence in context: A198337 A206483 A087011 * A000174 A156268 A053257 Adjacent sequences:  A294599 A294600 A294601 * A294603 A294604 A294605 KEYWORD nonn,easy AUTHOR Arkadiusz Wesolowski, Nov 03 2017 STATUS approved

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Last modified August 8 02:15 EDT 2020. Contains 336287 sequences. (Running on oeis4.)