A111014 Primes in the sequence A015519.

2, 11, 149, 2143, 6709949, 446049530175322600739691943

Offset: 1

Author

Cino Hilliard, Oct 02 2005

Keywords

• easy
• nonn

Comments

Is there an infinity of primes in this sequence?

References

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

Links

• Amiram Eldar, Table of n, a(n) for n = 1..9

Crossrefs

Cf. A015519.

Programs

Mathematica

Select[LinearRecurrence[{2, 7}, {0, 1}, 100], PrimeQ] (* Amiram Eldar, Jun 30 2024 *)

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+.) }

Formula

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)).