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 A111010 #22 Jul 04 2024 03:31:58
%S A111010 2,7,61,547,398581,23535794707,82064241848634269407
%N A111010 Primes of the form (3^k - (-1)^k)/4.
%C A111010 The next term is too large to include.
%C A111010 Is there an infinity of primes in this sequence?
%C A111010 All a(n), except a(1) = 2, are primes of the form (3^k + 1)/4. Corresponding numbers k such that (3^k + 1)/4 is prime are listed in A007658(n) = {3, 5, 7, 13, 23, 43, 281, 359, 487, 577, ...}. All such numbers k are primes. a(1) = 2 is the only prime of the form (3^k - 1)/4. - _Alexander Adamchuk_, Nov 19 2006
%D A111010 John Derbyshire, Prime Obsession, Joseph Henry Press, April 2004, p. 16.
%H A111010 Amiram Eldar, <a href="/A111010/b111010.txt">Table of n, a(n) for n = 1..14</a> (terms 1..11 from Alexander Adamchuk, Nov 19 2006)
%F A111010 Given a(0)=1, b(0)=1, then for i=1, 2, ..., a(i)/b(i) = (a(i-1) + 2*b(i-1)) /(a(i-1) + b(i-1)).
%F A111010 a(n) = A015518(A007658(n-1)) for n >= 2. - _Amiram Eldar_, Jul 04 2024
%t A111010 Do[f=(3^n - (-1)^n)/4; If[PrimeQ[f],Print[{n,f}]],{n,1,577}] (* _Alexander Adamchuk_, Nov 19 2006 *)
%o A111010 (PARI) primenum(n,k,typ) = /* k=mult,typ=1 num,2 denom. ouyput prime num or denom. */ { local(a,b,x,tmp,v); a=1;b=1; for(x=1,n, tmp=b; b=a+b; a=k*tmp+a; if(typ==1,v=a,v=b); if(isprime(v),print1(v","); ) ); print(); print(a/b+.); }
%Y A111010 Cf. A007658, A015518.
%K A111010 nonn
%O A111010 1,1
%A A111010 _Cino Hilliard_, Oct 02 2005
%E A111010 Edited by _Alexander Adamchuk_, Nov 19 2006