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A303971 Primes p such that 2*p + 1 and (5*p^2 + 4*p + 1)/2 are prime. 1
3, 5, 29, 53, 83, 173, 233, 239, 359, 653, 719, 743, 1013, 1583, 1889, 2129, 2399, 2939, 2969, 3299, 3359, 3413, 3449, 3539, 3863, 4073, 5399, 5639, 6323, 6983, 7433, 7643, 7649, 8243, 10613, 11369, 11519, 11699, 12119, 12653, 12923, 13463, 13619, 13649, 14303, 14489, 15629, 16253, 17333 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

(5*p^2 + 4*p + 1)/2 is equivalent to (A005384(k)^2 + A005385(k)^2)/2 for Sophie Germain primes and their safe primes whenever a particular k produces a prime.

a(n) == 5 (mod 6) for n > 1. a(n) == 23 or 29 (mod 30) for n > 2. - Robert Israel, May 08 2018

LINKS

Robert Israel, Table of n, a(n) for n = 1..10000

EXAMPLE

For p = A005384(3) = 5, (5*5^2 + 4*5 + 1)/2 = 73, which is prime, so 5 is in the sequence.

MAPLE

select(p -> isprime(p) and isprime(2*p+1) and isprime((5*p^2+4*p+1)/2),

[3, 5, seq(seq(30*i+j, j=[23, 29]), i=0..1000)]); # Robert Israel, May 08 2018

MATHEMATICA

Select[Prime[Range[2000]], AllTrue[{2#+1, (5#^2+4#+1)/2}, PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, May 19 2019 *)

PROG

(PARI) select(p->p<>2 && isprime(2*p+1) && isprime((5*p^2+4*p+1)/2), primes(3000)) \\ Andrew Howroyd, May 03 2018

CROSSREFS

Subsequence of A005384 and so of A000040.

Cf. A005385.

Sequence in context: A346659 A067200 A106089 * A136085 A153413 A257718

Adjacent sequences:  A303968 A303969 A303970 * A303972 A303973 A303974

KEYWORD

nonn,easy

AUTHOR

J. M. Bergot, May 03 2018

STATUS

approved

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Last modified December 6 16:17 EST 2021. Contains 349567 sequences. (Running on oeis4.)