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A274609 Primes p such that both 2p-1 and 2p^2-2p+1 are prime. 2
2, 3, 31, 331, 1171, 2011, 2281, 3181, 4621, 4861, 6151, 6211, 6961, 7951, 8521, 9151, 11251, 12211, 13411, 15661, 17491, 18121, 19141, 20641, 22531, 23071, 23581, 24631, 25411, 26041, 26161, 26431, 26641, 27091, 27271, 27361, 27691, 28201, 28621, 29221, 31891, 33151, 34261, 35491, 36451 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
All values of a(n), except {2,3}, are equal to 1 mod 30.
These are also primes p such that both p^2+c and p^2-c are positive primes, for some c, when c is a square, since that requires c = (p-1)^2. Corresponding c values begin {1, 4, 900, 108900, ...}. This relates to a comment at A047222.
LINKS
Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
EXAMPLE
31^2 - 30^2 = 61 and 31^2 + 30^2 = 1861 are both prime.
MATHEMATICA
result = {}; Do[If[PrimeQ[2*Prime[i] - 1] && PrimeQ[2*Prime[i]^2 - 2*Prime[i] + 1], AppendTo[result, Prime[i]]], {i, 1, 10000}]; result
Select[Prime[Range[4000]], AllTrue[{2#-1, 2#^2-2#+1}, PrimeQ]&] (* Harvey P. Dale, Dec 26 2022 *)
PROG
(PARI) is(n)=isprime(2*n-1) && isprime(2*n^2-2*n+1) && isprime(n) \\ Charles R Greathouse IV, Jul 15 2016
CROSSREFS
Cf. A047222.
Sequence in context: A347332 A054551 A049065 * A372142 A128030 A239593
KEYWORD
nonn
AUTHOR
Richard R. Forberg, Jun 30 2016
STATUS
approved

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Last modified June 19 19:50 EDT 2024. Contains 373507 sequences. (Running on oeis4.)