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A290283 Primes p such that A215458(p) is prime. 0
3, 5, 7, 11, 17, 19, 23, 101, 107, 109, 113, 163, 283, 311, 331, 347, 359, 701, 1153, 1597, 1621, 2063, 2437, 2909, 3319, 6011, 12829, 46147, 46471, 74219, 112297, 128411, 178693, 223759, 268841, 407821, 526763, 925391, 927763 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Primes p such that (2^p - (1/2 - (i * sqrt(7))/2)^p - (1/2 + (i * sqrt(7))/2)^p + 1)/2 is prime.
It is conjectured that there are infinitely many terms.
LINKS
EXAMPLE
A215458(3) = 7, A215458(5) = 11, A215458 (7) = 71 are all primes, hence 3, 5, 7 are in this sequence.
MAPLE
h := proc(n) option remember; `if`(n=0, 2, `if`(n=1, 1, h(n-1)-2*h(n-2))) end:
select(n->isprime((2^n-h(n)+1)/2), select(isprime, [$1..1000])); # Peter Luschny, Jul 26 2017
MATHEMATICA
Function[s, Keys@ KeySelect[s, AllTrue[{#, Lookup[s, #]}, PrimeQ] &]]@ MapIndexed[First[#2] - 1 -> #1 &, LinearRecurrence[{4, -7, 8, -4}, {0, 1, 4, 7}, 7000]] (* Michael De Vlieger, Jul 26 2017 *)
PROG
(PARI) isprime(([0, 1, 0, 0; 0, 0, 1, 0; 0, 0, 0, 1; -4, 8, -7, 4]^n*[0; 1; 4; 7])[1, 1])
CROSSREFS
Cf. A215458.
Sequence in context: A158361 A342692 A048184 * A163420 A155489 A194099
KEYWORD
nonn,more
AUTHOR
Paul S. Vanderveen, Jul 25 2017
STATUS
approved

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Last modified May 21 05:34 EDT 2024. Contains 372728 sequences. (Running on oeis4.)