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A270617
Primes p such that A256832(p) is divisible by p.
2
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
KEYWORD
nonn
AUTHOR
Altug Alkan, Mar 20 2016
STATUS
approved