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A247981
Primes dividing nonzero terms in A003095: the iterates of x^2 + 1 starting at 0.
13
2, 5, 13, 41, 137, 149, 229, 293, 397, 509, 661, 677, 709, 761, 809, 877, 881, 1217, 1249, 1277, 1601, 2053, 2633, 3637, 3701, 4481, 4729, 5101, 5449, 5749, 5861, 7121, 7237, 7517, 8009, 8089, 8117, 8377, 9661, 14869, 14897, 18229, 19609, 20369, 20441, 21493, 22349, 23917, 24781, 24977, 25717
OFFSET
1,1
COMMENTS
Relative density in the primes is 0, see Jones theorem 5.5.
LINKS
Charles R Greathouse IV, Table of n, a(n) for n = 1..500
Rafe Jones, The density of prime divisors in the arithmetic dynamics of quadratic polynomials, J. Lond. Math. Soc. (2) 78 (2) (2008), pp. 523-544.
FORMULA
a(n) << exp(k^n) for some constant k > 0, see Jones theorem 6.1. In particular this sequence is infinite. - Charles R Greathouse IV, Sep 28 2014
EXAMPLE
2 and 13 are in the sequence since A003095(4) = 26. 3 is not in the sequence since it does not divide any member of A003095.
MATHEMATICA
Select[Table[d=0; t=0; Do[t=Mod[t^2+1, Prime[j]]; If[t==0, d=1], {k, 1, Prime[j]}]; If[d==1, Prime[j], 0], {j, 1, 1000}], #!=0&] (* Vaclav Kotesovec, Oct 04 2014 *)
PROG
(PARI) is(p)=my(v=List([1]), t=1); while(t, t=(t^2+1)%p; for(i=1, #v, if(v[i]==t, return(0))); listput(v, t)); isprime(p)
CROSSREFS
KEYWORD
nonn
AUTHOR
STATUS
approved