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 A060392 #21 Feb 16 2025 08:32:44
%S A060392 0,1,5,47,11,221,17,1217,941,2747,8081,9281,41,55661,19421,333491,
%T A060392 1262201,601037,5237651,9063641,12899891,26149427,24073871,28537121,
%U A060392 352031501,398878547,160834691,67374467,146452961,24169417397
%N A060392 Let f(m) = smallest prime that divides k^2 + k + m for k = 0,1,2,...; sequence gives smallest m >= 0 such that f(m) is the n-th prime.
%C A060392 Chris Nash (see the Prime Puzzles link) has shown that such an m always exists.
%C A060392 For n>1, least odd number d such that the Legendre symbol (1-4d/prime(k)) = -1 for k = 2,...,n, but not for n+1. - _T. D. Noe_, Apr 19 2004
%D A060392 R. F. Lukes, C. D. Patterson and H. C. Williams, Numerical sieving devices: their history and some applications. Nieuw Arch. Wisk. (4) 13 (1995), no. 1, 113-139. Math. Rev. 96m:11082
%H A060392 G. W. Fung and H. C. Williams, <a href="https://doi.org/10.1090/S0025-5718-1990-1023759-3">Quadratic polynomials with high density of primes</a>, Mathematics of Computation, Vol. 55, 1990.
%H A060392 C. Rivera, <a href="http://www.primepuzzles.net/conjectures/conj_017.htm">www.primepuzzles.net, Conjecture 17</a>
%H A060392 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Prime-GeneratingPolynomial.html">Prime-Generating Polynomial</a>
%e A060392 k^2 + k takes the values 0, 2, 6, 12, ... for k = 0,1,2,...; the smallest prime divisor of these numbers is 2, so f(0) = 2.
%t A060392 nn=20; a=Table[0, {nn}]; d=-1; While[Length[Select[a, # == 0&]] != 1, d=d+2; i=2; While[JacobiSymbol[1-4d, Prime[i]]==-1, i++ ]; If[i<=nn && a[[i]]==0, a[[i]]=d]]; a (* corrected by _Jean-François Alcover_, Feb 06 2019 *)
%o A060392 (PARI) lista(nn) = {va = vector(nn); d = -1; while (#select(x->(x==0), va) != 1, d += 2; i = 2; while(kronecker(1-4*d, prime(i)) == -1, i++); if ((i <= nn) && (va[i] == 0), va[i] = d);); va;} \\ _Michel Marcus_, Feb 05 2019
%Y A060392 Cf. A060380, A060393-A060398. A060394 gives associated values of k.
%K A060392 nice,nonn
%O A060392 1,3
%A A060392 Luis Rodriguez-Torres (ludovicusmagister(AT)yahoo.com), Apr 03 2001
%E A060392 Corrected by _T. D. Noe_, Apr 19 2004