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 A279883 #10 Sep 15 2022 11:46:12 %S A279883 2,17,185302018885184100000000000000000000000000000001 %N A279883 Primes of the form (prime(j)-1)^(prime(j)+1) + 1. %C A279883 Prime terms from A279884. %C A279883 If a(4) exists, it must be bigger than (prime(2200)-1)^(prime(2200)+1) + 1 = 19422^19424 + 1. %C A279883 Corresponding pairs of numbers (j, prime(j)): (1, 2); (2, 3); (11, 31); ... %C A279883 It is extremely unlikely that a(4) exists. The term a(1)=1^3+1 is special. For other terms, note that b^k+1 can only be prime if k is a power of 2, so say k=2^p. Otherwise, if k has an odd factor, b^k+1 is algebraically factorizable. Therefore terms a(2) and later are of form (2^p-2)^(2^p)+1 with the additional obstruction that 2^p-1 must be a prime (namely a Mersenne prime), meaning that p (the exponent of the exponent) must be prime. With generalized Fermat numbers b^(2^p)+1 already primality tested to a high limits, the first undecided possibility for a(4) is 2147483646^2147483648+1 (has j=105097565 and p=31). - _Jeppe Stig Nielsen_, Sep 15 2022 %o A279883 (Magma) [(NthPrime(n)-1)^(NthPrime(n)+1)+1: n in[1..200] | IsPrime((NthPrime(n)-1)^(NthPrime(n)+1)+1)] %o A279883 (PARI) print1(1^3+1,", ");forprime(p=2,19,if(isprime(2^p-1),a=(2^p-2)^(2^p)+1;ispseudoprime(a)&&print1(a,", "))) \\ _Jeppe Stig Nielsen_, Sep 15 2022 %Y A279883 Cf. A000040, A279884. %K A279883 nonn,bref %O A279883 1,1 %A A279883 _Jaroslav Krizek_, Dec 21 2016