OFFSET
0,4
COMMENTS
See A225768 for motivation and references.
EXAMPLE
a(4)=1 because 1^4+4=5 is prime. (Although x^4+4 = (x^2-2*x+2)(x^2+2x+2), this is prime for x=1 when the first factor equals 1.)
a(5)=6 because 1^4+5=6, 2^4+5=21, 3^4+5=86, 4^4+5=261 and 5^4+5 are all composite, but 6^4+5=1301 is prime.
a(64)=0 because x^4+64 = (x^2-4*x+8)(x^2+4x+8) is composite for all integer values of x>0. Indeed, x^2-4x+8=(x-2)^2+4 > 1 for all x.
PROG
(PARI) {(a, b=4)->#factor(x^b+a)~==1&for(n=1, 9e9, ispseudoprime(n^b+a)&return(n)); a==1 || a==4 || print1("/*"factor(x^b+a)"*/")} \\ For illustrative purpose only. The polynomial is factored to avoid an infinite search loop when it is composite. But a factored polynomial can yield a prime when all but one factors equal 1. This happens for n=4, cf. Example.
CROSSREFS
KEYWORD
nonn
AUTHOR
M. F. Hasler, Jul 25 2013
STATUS
approved