cp's OEIS Frontend

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

%I A270617 #16 Mar 31 2017 01:11:37
%S A270617 2,5,7,13,17,23,29,31,37,41,47,53,59,61,71,73,79,89,97,101,103,109,
%T A270617 113,127,137,149,151,157,167,173,179,181,191,193,197,199,223,227,229,
%U A270617 233,239,241,251,257,263,269,271,277,281,293,311,313,317,337,349,353,359,367,373,379,383,389,397
%N A270617 Primes p such that A256832(p) is divisible by p.
%C A270617 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.
%H A270617 Charles R Greathouse IV, <a href="/A270617/b270617.txt">Table of n, a(n) for n = 1..10000</a>
%e A270617 5 is a term because A256832(5) = 3480 is divisible by 5.
%t A270617 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 *)
%o A270617 (PARI) a000129(n) = ([2, 1; 1, 0]^n)[2, 1];
%o A270617 t(n) = prod(k=1, n, Mod(a000129(k), n));
%o A270617 forprime(p=2, 1e3, if(lift(t(p)) == 0, print1(p, ", ")));
%o A270617 (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
%o A270617 (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
%Y A270617 Cf. A000129, A256832, A213891.
%K A270617 nonn
%O A270617 1,1
%A A270617 _Altug Alkan_, Mar 20 2016