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 A286682 #23 Jun 02 2025 12:21:57 %S A286682 1,4,12,4,22,12,114,4,138,142,2956,6388,5248,17532,96930,83782,1464, %T A286682 897448,300832,26908 %N A286682 a(n) = A059784(n+1) - A059784(n)^2. %C A286682 This sequence relates to A059784 just like A108739 relates to the Mills primes A051254. %C A286682 That this leads to a Mills-like real constant C such that floor(C^2^n) is a prime number for any natural number n, requires a proof of Legendre's conjecture that there is always a prime between consecutive perfect squares. %C A286682 a(18) and a(19) generate 96042- and 192083-decimal digit probable primes. - _Serge Batalov_, May 27 2024 %C A286682 a(20) generates a 384166-decimal digit probable prime. - _Serge Batalov_, May 27 2024 %e A286682 A059784(8) by construction can be written ((((((2^2 + 1)^2 + 4)^2 + 12)^2 + 4)^2 + 22)^2 + 12)^2 + 114. Taking out the addends gives 1, 4, 12, 4, 22, 12, 114 which lists the first seven terms of this sequence. %t A286682 Map[#2 - #1^2 & @@ # &, Partition[NestList[NextPrime[#^2] &, 2, 12], 2, 1]] (* _Michael De Vlieger_, May 12 2017 *) %o A286682 (PARI) p=2;while(1,a=nextprime(p^2);print1(a-p^2,", ");p=a) %Y A286682 Cf. A059784, A108739, A051254. %K A286682 nonn,hard,more %O A286682 1,2 %A A286682 _Jeppe Stig Nielsen_, May 12 2017 %E A286682 a(14)-a(17) from _Serge Batalov_, May 26 2024 %E A286682 a(18)-a(20) from _Serge Batalov_, May 27 2024