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.
%I A145281 #13 May 24 2021 06:43:17
%S A145281 2,3,3,3,5,5,11,11,13,17,19,23,29,29,31,37,41,41,47,53,53,59,61,67,73,
%T A145281 79,79,83,83,89,101,101,107,109,127,127,127,131,137,139,149,149,157,
%U A145281 157,163,163,173,191,191,191,193,199,211,211,223,223,227,227,233,239
%N A145281 a(n) is the least prime such that (ceiling(sqrt(a(n)*p_n)))^2 - a(n)*p_n is a perfect square, where p_n is the n-th prime.
%C A145281 Theorem. p_n - 2*sqrt(2p_n) + 2<a(n) <= p_n. Corollary. a(n)~n*log(n). Conjecture. a(n) is the nearest prime p >= A145236(n).
%C A145281 Or a(n) is the least prime q_n <= p_n such that sqrt(p_n) - sqrt(q_n) < sqrt(2) [or (p_n + q_n)/2 < sqrt(p_n*q_n) + 1]. See also our comment to A145300. - _Vladimir Shevelev_, Oct 09 2008
%C A145281 The above conjecture is true. This means that a(n) is the nearest prime p > p_n - 2*floor(sqrt(2*p_n)) + 2. A considerably more important and deep question is whether p < p_n. The answer does not follow even from the Riemann conjecture about zeros of the zeta function. - _Vladimir Shevelev_, Oct 17 2008
%o A145281 (PARI) a(n) = {my(p = prime(n)); my(q = 2); while (! issquare(ceil(sqrt(q*p))^2 - q*p), q = nextprime(q+1)); q;} \\ _Michel Marcus_, Jul 06 2015
%Y A145281 Cf. A145236, A000040, A145016, A145022, A145023, A145047, A145048, A145049, A045050.
%K A145281 nonn
%O A145281 1,1
%A A145281 _Vladimir Shevelev_, Oct 06 2008, Oct 07 2008
%E A145281 More terms from _Michel Marcus_, Jul 06 2015