A270617 Primes p such that A256832(p) is divisible by p.

2, 5, 7, 13, 17, 23, 29, 31, 37, 41, 47, 53, 59, 61, 71, 73, 79, 89, 97, 101, 103, 109, 113, 127, 137, 149, 151, 157, 167, 173, 179, 181, 191, 193, 197, 199, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 293, 311, 313, 317, 337, 349, 353, 359, 367, 373, 379, 383, 389, 397

Offset: 1

Author

Altug Alkan, Mar 20 2016

Keywords

• nonn

Comments

Sequence focuses on the prime numbers because of the complement of this sequence. Primes that are listed in this sequence cannot be generated by function which is related with A213891. See comment section of A213891.

Examples

			5 is a term because A256832(5) = 3480 is divisible by 5.
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000129, A256832, A213891.

Programs

Mathematica

nn = 400; s = FoldList[Times, LinearRecurrence[{2, 1}, {1, 2}, nn]]; Select[Prime@ Range@ PrimePi@ nn, Divisible[s[[#]], #] &] (* Michael De Vlieger, Mar 27 2016, after Harvey P. Dale at A256832 *)

PARI

a000129(n) = ([2, 1; 1, 0]^n)[2, 1];
t(n) = prod(k=1, n, Mod(a000129(k), n));
forprime(p=2, 1e3, if(lift(t(p)) == 0, print1(p, ", ")));

PARI

is(n)=my(a=Mod(1,n),b=Mod(2,n)); for(i=2,n, if(b==0, return(isprime(n))); [a,b]=[b,2*b+a]); 0 \\ Charles R Greathouse IV, Mar 31 2016

PARI

list(lim)=my(v=List([2]), G=factorback(primes([2,lim])), a=1, b=2, t=2, p=2); forprime(q=3,lim, for(n=p+1,q, [a,b]=[b,2*b+a]; t=gcd(t*b, G)); if(t%q==0, listput(v, q)); G/=q; p=q); Vec(v) \\ Charles R Greathouse IV, Mar 31 2016