A176117 Primes p such that T(p) is prime in Juricevic conjecture on classification of Lehmer triples.

2, 5, 809

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

Table of n, a(n) for n=1..3.

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

Cf. A000040.

Sequence in context: A240768 A212590 A208212 * A369022 A078748 A051131

Adjacent sequences: A176114 A176115 A176116 * A176118 A176119 A176120

Keyword

bref,more,nonn

Author

Jonathan Vos Post, Apr 08 2010

Status

approved