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%I #31 Sep 08 2022 08:45:12
%S 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,
%T 31,25,23,30,32,30,29,31,32,34,30,34,40,32,36,39,37,37,40,38,39,44,42,
%U 45,44,42,42,45,42,48,52,49,45,50,48,51,55,56,47,52,56,56,53,49,58,62,56
%N Number of primes between squares of successive odd numbers.
%C 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 n-th square ring around 1 of the Ulam spiral. - _Scott R. Shannon_, Jan 14 2020
%H Didier van der Straten, Jon Perry, Mark Underwood, <a href="/A089166/a089166.txt">TR: [PrimeNumbers] pi(x)</a>, digest of 3 messages in primeforms Yahoo group, Aug 29 - Aug 30, 2003. [Cached copy]
%H Mark Underwood, <a href="http://groups.yahoo.com/group/primenumbers/message/13421">[PrimeNumbers] pi(x)</a>.
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Ulam_spiral">Ulam Spiral</a>.
%t Table[PrimePi[(2n + 1)^2] - PrimePi[(2n - 1)^2], {n, 1, 72}]
%o (PARI) forstep (k=1,130,2,print1(primepi((k+2)^2)-primepi(k^2),", ")) \\ _Hugo Pfoertner_, Nov 15 2019
%o (Magma) [#[p:p in PrimesInInterval(k^2,(k+2)^2)]:k in [1..150 by 2]]; // _Marius A. Burtea_, Jan 14 2020
%Y Cf. A014085, A016754 (odd squares).
%K nonn
%O 1,1
%A _Robert G. Wilson v_, Dec 06 2003
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