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 A235364 #29 Feb 16 2025 08:33:21 %S A235364 29,31,857,859,1721,1723 %N A235364 Twin primes p, p+2 such that p+1 is a Giuga number. %C A235364 For all 12 known Giuga numbers N, either both N-1 and N+1 are prime or neither is prime. Is it true that if any Giuga number N is adjacent to a prime N-1 or N+1, then in fact N lies between twin primes N-1, N+1? %C A235364 See A235139 for a similar property of the known primary pseudoperfect numbers. %C A235364 A007850 lists a 13th in its comments. - _Bill McEachen_, Jan 14 2014 %C A235364 If g = 420001794970774706203871150967065663240419575375163060922876441614\ 2557211582098432545190323474818 is confirmed as the 13th Giuga number, it will not be between a(7) and a(8), because g-1 is divisible by 13. So a(7) is not equal to g-1. But g+1 is prime (certified using the APRCL test in PARI) so g provides a negative answer to the above question. - _Ralf Stephan_, Jan 20 2014 (corrected by _Jonathan Sondow_, Jan 21 2014) %C A235364 (Revision of my question.) For all 13 known Giuga numbers N, if N-1 is prime, then N+1 is also prime. Is it true that if any Giuga number N is 1 more than a prime, then N lies between twin primes N-1, N+1? - _Jonathan Sondow_, Mar 02 2014 %H A235364 MathWorld, <a href="https://mathworld.wolfram.com/GiugaNumber.html">Giuga Number</a> %H A235364 Wikipedia, <a href="http://en.wikipedia.org/wiki/Giuga_number">Giuga number</a> %e A235364 For the twin primes (p,p+2) = (29, 31), (857, 859), (1721, 1723), the numbers p+1 = 30, 858, 1722 are Giuga numbers (A007850). %Y A235364 Cf. A007850, A235139. %K A235364 nonn,more,hard %O A235364 1,1 %A A235364 _Jonathan Sondow_, Jan 07 2014