A064483 Numbers k such that k^2 + prime(k) and k^2 - prime(k) are both primes.

12, 30, 60, 96, 336, 660, 702, 756, 984, 990, 1188, 1302, 1488, 1830, 1866, 2070, 2142, 2340, 2586, 2874, 2910, 3618, 3714, 3750, 3774, 3906, 4008, 4470, 4512, 4902, 5094, 5754, 6012, 6174, 6432, 6840, 6846, 6930, 7446, 7578, 7734, 8064, 8190, 8328

Offset: 1

Author

Robert G. Wilson v and Jason Earls, Oct 05 2001

Keywords

• easy
• nonn

Comments

All terms are multiples of 6. - Jon E. Schoenfield, Apr 13 2024

Examples

			12 is in the sequence because 144 +/- 37 = 181 and 107 which are both primes.
k=30 is a term: 30^2 = 900, prime(30) = 113, 900+113 = 1013 and 900-113 = 787, both primes.
		

Links

• Zak Seidov, Table of n, a(n) for n = 1..10000 (first 1000 terms from Harry J. Smith)

Crossrefs

Intersection of A064711 and A064712. - Zak Seidov, Oct 12 2014

Programs

Mathematica

Select[ Range[10^4], PrimeQ[ #^2 + Prime[ # ]] && PrimeQ[ #^2 - Prime[ # ]] &]

PARI

for(n=1,20000, if(isprime(n^2+prime(n)) && isprime(n^2-prime(n)), print1(n," ")))

PARI

{ n=0; default(primelimit, 6100000); for (m=1, 10^9, if (isprime(m^2 + prime(m)) && isprime(m^2 - prime(m)), write("b064483.txt", n++, " ", m); if (n==1000, break)) ) } \\ Harry J. Smith, Sep 16 2009