A241101 -id:A241101

Search: a241101 -id:a241101

Displaying 1-2 of 2 results found.

page 1

A241120

Primes p such that (p^3 + 2)/3 is prime.

+10
4

13, 19, 31, 193, 211, 223, 229, 271, 331, 571, 619, 691, 739, 751, 853, 991, 1009, 1039, 1051, 1231, 1303, 1321, 1549, 1741, 1789, 1831, 1993, 1999, 2029, 2089, 2113, 2143, 2203, 2311, 2521, 2551, 2683, 2749, 2851, 3121, 3259, 3331, 3571, 3631, 3823, 3853, 4093

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

LINKS

K. D. Bajpai, Table of n, a(n) for n = 1..8879

EXAMPLE

13 is prime and appears in the sequence because (13^3 + 2)/3 = 733 which is a prime.

31 is prime and appears in the sequence because (31^3 + 2)/3 = 9931 which is a prime.

MAPLE

KD:= proc() local a, b; a:=ithprime(n); b:=(a^3+2)/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 + 2)/3] &]

n = 0; Do[If[PrimeQ[(Prime[k]^3 + 2)/3], n = n + 1; Print[n, " ", Prime[k]]], {k, 1, 200000}] (* b-file *)

PROG

(PARI) s=[]; forprime(p=2, 8000, if((p^3+2)%3==0 && isprime((p^3+2)/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).

Cf. A241101 (primes p: (p^3-4)/3 is prime).

KEYWORD

nonn

AUTHOR

K. D. Bajpai, Apr 16 2014

STATUS

approved

A235705

Primes p such that (p^3 + 6)/5 is prime.

+10
1

19, 59, 269, 349, 409, 419, 479, 769, 929, 1109, 1319, 1399, 1979, 2609, 3659, 4079, 4919, 5309, 5449, 5879, 6079, 6299, 6949, 7069, 7129, 7229, 7699, 7829, 8069, 8329, 8599, 9679, 10729, 11969, 12809, 13109, 13229, 13859, 14159, 14419, 14629, 14929, 15259

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

All the terms in the sequence are congruent to 1 or 3 mod 4.

LINKS

K. D. Bajpai, Table of n, a(n) for n = 1..2640

EXAMPLE

a(1) = 19 is prime: (19^3 + 6)/ 5 = 1373 which is also prime.

a(2) = 59 is prime: (59^3 + 6)/ 5 = 41077 which is also prime.

MAPLE

KD:= proc() local a, b; a:=ithprime(n); b:=(a^3+6)/5; if b=floor(b) and isprime(b) then RETURN (a); fi; end: seq(KD(), n=1..5000);

MATHEMATICA

Select[Prime[Range[5000]], PrimeQ[(#^3 + 6)/5] &]

n = 0; Do[If[PrimeQ[(Prime[k]^3 + 6)/5], n = n + 1; Print[n, " ", Prime[k]]], {k, 1, 200000}] (*b-file*)