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 A089609 Prime number of primes between squares of consecutive primes; or, primes occurring in A050216. 3
 2, 5, 11, 47, 163, 89, 463, 479, 199, 107, 241, 151, 709, 151, 599, 313, 547, 211, 613, 859, 863, 241, 1217, 1091, 827, 311, 967, 1327, 691, 1109, 1123, 829, 389, 821, 857, 431, 1301, 433, 1451, 1933, 3449, 5701, 1753, 4663, 563, 3557, 4253, 1867, 4447 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS For small values of n, these numbers exhibit higher and lower values as n increases. Conjecture: There exists an n such that seq(n1) is < seq(n1+1) for all n1 >= n. LINKS Harvey P. Dale, Table of n, a(n) for n = 0..1000 MATHEMATICA Select[PrimePi[#[[2]]]-PrimePi[#[[1]]]&/@Partition[Prime[Range[500]]^2, 2, 1], PrimeQ] (* Harvey P. Dale, May 15 2022 *) PROG (PARI) \ prime number of primes between squares. pbetweensq(n) = { for(x=1, n, c=0; for(y=prime(x)^2, prime((x+1))^2, if(isprime(y), c++) ); if(isprime(c), print1(c", ")) ) } CROSSREFS Cf. A000879, A050216. Sequence in context: A106887 A236044 A285809 * A277041 A087185 A127010 Adjacent sequences:  A089606 A089607 A089608 * A089610 A089611 A089612 KEYWORD easy,nonn AUTHOR Cino Hilliard, Dec 30 2003 EXTENSIONS Edited by Ray Chandler, Jan 05 2004 STATUS approved

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Last modified July 4 04:47 EDT 2022. Contains 355064 sequences. (Running on oeis4.)