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%I #12 Mar 08 2015 19:32:36
%S 2,7,61,547,398581,23535794707,82064241848634269407
%N Primes of the form (3^k - (-1)^k)/4.
%C The next term is too large to include.
%C Is there an infinity of primes in this sequence?
%C 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 Prime Obsession, John Derbyshire, Joseph Henry Press, April 2004, p 16.
%H Alexander Adamchuk, Nov 19 2006, <a href="/A111010/b111010.txt">Table of n, a(n) for n = 1..11</a>
%F 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)).
%t Do[f=(3^n - (-1)^n)/4; If[PrimeQ[f],Print[{n,f}]],{n,1,577}] (* _Alexander Adamchuk_, Nov 19 2006 *)
%o (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 Cf. A007658, A015518.
%K nonn
%O 1,1
%A _Cino Hilliard_, Oct 02 2005
%E Edited by _Alexander Adamchuk_, Nov 19 2006
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