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 A335135 Number of composite numbers between prime(n)^2 and prime(n + 1)^2 - 1. 1
 3, 11, 18, 57, 39, 98, 61, 141, 265, 104, 351, 268, 148, 314, 520, 594, 208, 678, 486, 258, 806, 573, 918, 1325, 703, 366, 753, 390, 788, 3006, 933, 1443, 503, 2581, 542, 1666, 1734, 1192, 1842, 1917, 644, 3364, 691, 1416, 717, 4457, 4729 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS Robert Israel, Table of n, a(n) for n = 1..2000 FORMULA a(n) = prime(n + 1)^2 - prime(n)^2 - (pi(prime(n + 1)^2) - pi(prime(n)^2)). EXAMPLE For n = 1 prime(1) = 2 and prime(2) = 3. So the composite numbers between 2^2 = 4 and 3^2 - 1 = 9 - 1 = 8 are 4, 6, 8 ie 3 and a(1) = 3. MAPLE f:= proc(n) local p, q; p:= ithprime(n); q:= nextprime(p); q^2 - p^2 - numtheory:-pi(q^2)+numtheory:-pi(p^2) end proc: map(f, [\$1..50]); # Robert Israel, Jun 24 2020 MATHEMATICA Array[#1 - #2 - (PrimePi@ #1 - PrimePi@ #2) & @@ {Prime[# + 1]^2, Prime[#]^2} &, 47] (* Michael De Vlieger, May 24 2020 *) PROG (PARI) forprime(n = 2, 220, s = 0; forcomposite(k = n^2, nextprime(n + 1)^2 - 1, s++); print1(s", ")) CROSSREFS Cf. A000040, A002808. Sequence in context: A119141 A303520 A225144 * A228470 A246453 A117769 Adjacent sequences:  A335132 A335133 A335134 * A335136 A335137 A335138 KEYWORD nonn,look AUTHOR Dimitris Valianatos, May 24 2020 STATUS approved

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Last modified August 12 10:31 EDT 2020. Contains 336438 sequences. (Running on oeis4.)