cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A104269 Prime numbers p such that primepi(p) + p is a square.

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%I A104269 #23 Oct 27 2021 11:58:55
%S A104269 11,37,443,571,1049,1307,1451,1523,2837,3593,5233,8539,9257,9439,
%T A104269 10391,10987,17579,21881,23321,23909,25117,30557,30893,31231,42239,
%U A104269 47123,64811,65789,83089,91631,92219,95747,97549,99971,101197,101807,110603,114487,120431
%N A104269 Prime numbers p such that primepi(p) + p is a square.
%C A104269 A064371(p) + A000040(A064371(p)) = A086968(p)^2.
%C A104269 p^2 is prime + its index A086968; p + p-th prime is a square A064371.
%C A104269 Equals the prime terms of A073945. - _Bill McEachen_, Oct 26 2021
%F A104269 a(n) = A086968(n)^2 - pi(a(n)).
%e A104269 37 is a term because 37 is 12th prime and 37 + 12 = 49 = 7^2.
%p A104269 q:= n-> isprime(n) and issqr(n+numtheory[pi](n)):
%p A104269 select(q, [$0..150000])[];  # _Alois P. Heinz_, Oct 27 2021
%t A104269 Select[Prime@Range[10^4],IntegerQ@Sqrt[PrimePi@#+#]&] (* _Giorgos Kalogeropoulos_, Oct 26 2021 *)
%o A104269 (PARI) isok(n) = isprime(n) && issquare(n + primepi(n)); \\ _Michel Marcus_, Oct 05 2013
%Y A104269 Cf. A000040, A000720, A064371, A086968, A064370, A073945.
%K A104269 nonn
%O A104269 1,1
%A A104269 _Zak Seidov_, Feb 26 2005
%E A104269 Definition corrected by _Michel Marcus_, Oct 05 2013