

A089166


Number of primes between squares of successive odd numbers.


3



4, 5, 6, 7, 8, 9, 9, 13, 11, 13, 14, 15, 15, 17, 16, 19, 19, 19, 21, 23, 20, 23, 23, 28, 21, 31, 25, 23, 30, 32, 30, 29, 31, 32, 34, 30, 34, 40, 32, 36, 39, 37, 37, 40, 38, 39, 44, 42, 45, 44, 42, 42, 45, 42, 48, 52, 49, 45, 50, 48, 51, 55, 56, 47, 52, 56, 56, 53, 49, 58, 62, 56
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OFFSET

1,1


COMMENTS

As the squares of the successive odd numbers are those numbers appearing on the SE spoke of the Ulam spiral, a(n) also gives the number of primes appearing in the nth square ring around 1 of the Ulam spiral.  Scott R. Shannon, Jan 14 2020


LINKS

Table of n, a(n) for n=1..72.
Didier van der Straten, Jon Perry, Mark Underwood, TR: [PrimeNumbers] pi(x), digest of 3 messages in primeforms Yahoo group, Aug 29  Aug 30, 2003. [Cached copy]
Mark Underwood, [PrimeNumbers] pi(x).
Wikipedia, Ulam Spiral.


MATHEMATICA

Table[PrimePi[(2n + 1)^2]  PrimePi[(2n  1)^2], {n, 1, 72}]


PROG

(PARI) forstep (k=1, 130, 2, print1(primepi((k+2)^2)primepi(k^2), ", ")) \\ Hugo Pfoertner, Nov 15 2019
(MAGMA) [#[p:p in PrimesInInterval(k^2, (k+2)^2)]:k in [1..150 by 2]]; // Marius A. Burtea, Jan 14 2020


CROSSREFS

Cf. A014085, A016754 (odd squares).
Sequence in context: A090925 A143836 A168094 * A178052 A030543 A214084
Adjacent sequences: A089163 A089164 A089165 * A089167 A089168 A089169


KEYWORD

nonn


AUTHOR

Robert G. Wilson v, Dec 06 2003


STATUS

approved



