A140454 -id:A140454

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A240110

Primes p such that p+2 and p^3+2 are also prime.

+10
4

3, 5, 29, 71, 311, 419, 431, 1031, 1091, 1151, 1451, 1931, 2339, 3371, 3461, 4001, 4421, 4799, 5651, 6269, 6551, 6569, 6761, 6779, 6869, 7559, 7589, 8219, 9011, 9281, 10301, 11069, 11489, 11549, 12161, 12239, 12251, 12539, 14081, 15641, 17189, 18059, 18119, 18521

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

OFFSET

1,1

COMMENTS

All the terms in the sequence, except a(1), are congruent to 2 mod 3.

LINKS

K. D. Bajpai, Table of n, a(n) for n = 1..3166

MAPLE

KD := proc() local a, b, d; a:=ithprime(n); b:=a+2; d:=a^3+2; if isprime(b)and isprime(d) then RETURN (a); fi; end: seq(KD(), n=1..10000);

MATHEMATICA

Select[Prime[Range[2200]], AllTrue[{#+2, #^3+2}, PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Mar 14 2017 *)

PROG

(PARI) s=[]; forprime(p=2, 20000, if(isprime(p+2) && isprime(p^3+2), s=concat(s, p))); s \\ Colin Barker, Apr 01 2014

CROSSREFS

Cf. A000040, A048637, A140454, A175234, A236687, A236688.

KEYWORD

nonn

AUTHOR

K. D. Bajpai, Apr 01 2014

STATUS

approved

A240126

Primes p such that p - 2 and p^3 - 2 are also prime.

+10
4

19, 31, 109, 151, 241, 619, 859, 1489, 1951, 2131, 2791, 2971, 3559, 4129, 4651, 4789, 4801, 5659, 6661, 6781, 7591, 8221, 8629, 8821, 8971, 9241, 9721, 9931, 10891, 11971, 12109, 12541, 13831, 14011, 15271, 15289, 15331, 16831, 17029, 17419, 17839, 17989, 18121, 18541, 20149, 20899, 21019

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

OFFSET

1,1

COMMENTS

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

LINKS

K. D. Bajpai, Table of n, a(n) for n = 1..3085

EXAMPLE

19 is in the sequence because 19 is a prime: 19 - 2 = 17 and 19^3 - 2 = 6857 are also prime.

151 is in the sequence because 151 is a prime: 151 - 2 = 149 and 151^3 - 2 = 3442949 are also prime.

MAPLE

KD := proc() local a, b, d; a:=ithprime(n); b:=a-2; d:=a^3-2; if isprime(b)and isprime(d) then RETURN (a); fi; end: seq(KD(), n=1..10000);

MATHEMATICA

Select[Prime[Range[2000]], PrimeQ[# - 2] && PrimeQ[#^3 - 2] &]

PROG

(PARI) s=[]; forprime(p=2, 22000, if(isprime(p-2) && isprime(p^3-2), s=concat(s, p))); s \\ Colin Barker, Apr 02 2014