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Primes in the sequence A015519.
1

%I #14 Jun 30 2024 03:22:45

%S 2,11,149,2143,6709949,446049530175322600739691943

%N Primes in the sequence A015519.

%C Is there an infinity of primes in this sequence?

%D John Derbyshire, Prime Obsession, Joseph Henry Press, April 2004, p. 16.

%H Amiram Eldar, <a href="/A111014/b111014.txt">Table of n, a(n) for n = 1..9</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 Select[LinearRecurrence[{2, 7}, {0, 1}, 100], PrimeQ] (* _Amiram Eldar_, Jun 30 2024 *)

%o (PARI) primenum(n,k,typ) = /* k=mult,typ=1 num,2 denom. output 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. A015519.

%K easy,nonn

%O 1,1

%A _Cino Hilliard_, Oct 02 2005