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