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

1,1

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.

Links

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

Example

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

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 *)

Prog

(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

Crossrefs

Cf. A000129, A256832, A213891.

Sequence in context: A023204 A248606 A252801 * A045352 A278494 A107426

Adjacent sequences: A270614 A270615 A270616 * A270618 A270619 A270620

Keyword

nonn

Author

Altug Alkan, Mar 20 2016

Status

approved