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 A273595 #38 Feb 16 2025 08:33:35
%S A273595 43,47,53,71,83,113,131,173,251,281,383,461,503,593,743,73361,73421,
%T A273595 3071069,15949847,76553693,2204597,1842719,246407807,986578883,
%U A273595 73975907,4069235123,1244414939,25213427,656856899,30641069183,8221946477,41730358853,10066886927,285340609997,6232338461
%N A273595 Least q > 0 such that min { x >= 0 | q + prime(n)*x + x^2 is composite } is a (local) maximum, cf. A273756 & A273770.
%C A273595 This is a subsequence of A273756 which considers all odd numbers (2n+1) instead of only prime(n) as coefficients of the linear term.
%C A273595 All terms are necessarily prime, since this is necessary and sufficient to get a prime for x = 0.
%C A273595 The respective minima (= number of consecutive primes for x = 0, 1, 2, ...) are given in A273597.
%C A273595 It has been pointed out by _Don Reble_ that the prime k-tuple conjecture predicts infinitely long sequences of primes of the given form, therefore we consider the "local" maxima, for q below some appropriate (large) limit: see sequences A273756 & A273770 for further details. - _M. F. Hasler_, Feb 17 2020
%H A273595 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Prime-GeneratingPolynomial.html">Prime-Generating Polynomial</a>.
%H A273595 <a href="/index/Pri">Index to entries related to primes produced by polynomials</a>.
%F A273595 a(n) = A273756((prime(n) - 1)/2). - _M. F. Hasler_, Feb 17 2020
%o A273595 (PARI) A273595(n)=A273756(prime(n)\2) \\ changed Feb 17 2020
%Y A273595 Cf. A273756, A273770.
%Y A273595 Cf. also A002837 (n such that n^2-n+41 is prime), A007634 (n such that n^2+n+41 is composite), A005846 (primes of form n^2+n+41), A097823, A144051, A187057 .. A187060, A190800, A191456 ff.
%K A273595 nonn
%O A273595 2,1
%A A273595 _M. F. Hasler_, May 26 2016
%E A273595 Edited and extended using A273756(0..100) due to _Don Reble_, by _M. F. Hasler_, Feb 17 2020