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A241101 Primes p such that (p^3 - 4)/3 is prime. 3
7, 31, 37, 43, 61, 73, 97, 103, 157, 163, 211, 277, 331, 337, 457, 487, 613, 661, 733, 751, 811, 883, 991, 1021, 1093, 1297, 1321, 1483, 1693, 1741, 1873, 2083, 2113, 2143, 2203, 2221, 2287, 2347, 2437, 2473, 2707, 2917, 3001, 3067, 3187, 3307, 3331, 3343, 3541 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

K. D. Bajpai, Table of n, a(n) for n = 1..8906

EXAMPLE

7 is prime and appears in the sequence because (7^3 - 4)/3 = 113 which is a prime.

31 is prime and appears in the sequence because (31^3 - 4)/3 = 9929 which is a prime.

MAPLE

KD:= proc() local a, b; a:=ithprime(n); b:=(a^3-4)/3; if b=floor(b) and isprime(b) then RETURN (a); fi; end: seq(KD(), n=1..1000);

MATHEMATICA

Select[Prime[Range[500]], PrimeQ[(#^3 - 4)/3] &]

n = 0; Do[If[PrimeQ[(Prime[k]^3 - 4)/3], n = n + 1; Print[n, " ", Prime[k]]], {k, 1, 200000}] (*b-file*)

PROG

(PARI) s=[]; forprime(p=2, 4000, if((p^3-4)%3==0 && isprime((p^3-4)/3), s=concat(s, p))); s \\ Colin Barker, Apr 16 2014

CROSSREFS

Cf. A109953 (primes p: (p^2+1)/3 is prime).

Cf. A118915 (primes p: (p^2+5)/6 is prime).

Cf. A118918 (primes p: (p^2+11)/12 is prime).

Sequence in context: A103630 A205711 A040064 * A238664 A272201 A325423

Adjacent sequences:  A241098 A241099 A241100 * A241102 A241103 A241104

KEYWORD

nonn

AUTHOR

K. D. Bajpai, Apr 16 2014

STATUS

approved

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Last modified November 29 12:24 EST 2021. Contains 349416 sequences. (Running on oeis4.)