A161500 Primes dividing some member of A073833.

2, 5, 29, 41, 89, 101, 109, 269, 421, 509, 521, 709, 929, 941, 1549, 1861, 2281, 2521, 2749, 2801, 2909, 3121, 3169, 3469, 5821, 5881, 7109, 8069, 8969, 9041, 9181, 10061, 10601, 11549, 15121, 16061, 16889, 16981, 21929, 30089, 30169, 32561, 41149

Offset: 1

Author

Franklin T. Adams-Watters, Jun 11 2009

Keywords

• nonn

Comments

Primes that divide A073833(n) will divide A073834(m) for any m > n, and this is all the prime divisors of A073834(m).

Iterating f(x) = x + 1/x modulo p will eventually either produce a zero (in which case p is in this sequence), or it will loop to an earlier term (in which case it is not). Since f(-x) = -f(x), encountering the negation of an earlier term means that the iteration is looping.

Note that A073833(6) = 969581 = 521 * 1861 is the first composite member of that sequence.

Crossrefs

Cf. A073833, A073834, A000057.

Programs

PARI

ina(p)=local(m,k,v);m=Mod(1,p);v=vector(p\2);while(m!=0,k=lift(m);if(2*k>p,k=p-k);if(v[k],return(0));v[k]=1;m+=1/m);1