OFFSET
1,1
COMMENTS
Tsumura: In paper on a classification of Lehmer triples, Juricevic conjectured that there are infinitely many primes of special form. We disprove one of his conjectures and consider the other one. Let us consider T(p). Now T(p) is not composite for all primes p. For example, T(p) is prime for p = 2, 5, 809. (These are the only primes the author found.) Although we neither prove nor disprove Conjecture 1.1, we can show that there are infinitely many primes p such that T(p) is composite.
Primes p such that A110035(2p) is prime. The value after 809 is > 2741. - R. J. Mathar, Jul 22 2010
a(4) >15661, if it exists. - D. S. McNeil, Nov 27 2010
LINKS
Robert Juricevic, Classifying Lehmer triples, Acta Arith. 137 (2009), no. 3, 207-232. MR MR2496461
Yu Tsumura, On compositeness of special types of integers, April 8, 2010.
FORMULA
{p such that T(p) is prime, where T(p) = (1/5)*(((1+sqrt(5))*((3+sqrt(5))/2)^(2*p)) + ((1-sqrt(5))*((3-sqrt(5))/2)^(2*p)) + 3).
CROSSREFS
KEYWORD
bref,more,nonn
AUTHOR
Jonathan Vos Post, Apr 08 2010
STATUS
approved