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 A138465 #21 May 04 2017 11:35:36 %S A138465 3,23,31,137,191,239,277,359,431,439,683,719,743,911,997,1031,1061, %T A138465 1103,1109,1223,1279,1423,1439,1481,1511,1559,1583,1597,1733,1873, %U A138465 2017,2039,2063,2351,2399,2411,2543,2683,2897,2903,3023,3347,3359,3457,3517,3607,3623,3793,3797 %N A138465 Non-optimus primes. %C A138465 A prime p is an optimus prime if (1 + sqrt( legendre(-1,p)*p ))^p - 1 = r + s*sqrt( legendre(-1,p)*p ) where gcd(r,s) = p. %D A138465 A. Slinko, Additive representability of finite measurement structures, in "The Mathematics of Preference, Choice and Order: Essays in Honor of Peter Fishburn", edited by Steven Brams, William V. Gehrlein and Fred S. Roberts, Springer, 2009, pp. 113-133. %H A138465 Charles R Greathouse IV, <a href="/A138465/b138465.txt">Table of n, a(n) for n = 1..5000</a> %H A138465 S. Marshall, <a href="http://www.sipta.org/isipta05/proceedings/papers/s030.pdf">On the existence of extremal cones and comparative probability orderings</a>, Proceedings of The 4th International Symposium on Imprecise Probabilities and Their Applications (ISIPTA 05), Pittsburg, Pennsylvania, 2005, pp. 246-255. %H A138465 Arkadii Slinko, <a href="http://www.math.auckland.ac.nz/~slinko/Research/survey5.pdf">Additive Representability of Finite Measurement Structures</a>, 2007, 26 pp. %H A138465 Arkadii Slinko, <a href="/A217090/a217090.pdf">Additive Representability of Finite Measurement Structures</a>, 2007, 26 pp. [Cached copy] %e A138465 For p = 13, (1 + sqrt( legendre(-1,p)*p ))^p - 1 = 209588223+58200064*13^(1/2), and gcd(209588223,58200064) = 13, so 13 is an optimus prime. %e A138465 For p = 23, (1 + sqrt( legendre(-1,p)*p ))^p - 1 = 7453766387236863-24397683359744*(-23)^(1/2), but gcd(7453766387236863,24397683359744) = 1081 != 23, so 23 is a non-optimus prime. %o A138465 (PARI) is(p)=if(p<3 || !isprime(p),return(0)); my(t=(2*quadgen(kronecker(-1,p)*p))^p);gcd(imag(t),real(t)-1)!=p \\ _Charles R Greathouse IV_, Sep 26 2012 %Y A138465 Cf. A217090 (optimus primes). %K A138465 nonn %O A138465 1,1 %A A138465 _N. J. A. Sloane_, Feb 07 2009 %E A138465 More terms from _Charles R Greathouse IV_, Sep 26 2012