A064483 - OEIS

%I #23 Apr 13 2024 14:58:23

%S 12,30,60,96,336,660,702,756,984,990,1188,1302,1488,1830,1866,2070,

%T 2142,2340,2586,2874,2910,3618,3714,3750,3774,3906,4008,4470,4512,

%U 4902,5094,5754,6012,6174,6432,6840,6846,6930,7446,7578,7734,8064,8190,8328

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

%C All terms are multiples of 6. - _Jon E. Schoenfield_, Apr 13 2024

%H Zak Seidov, <a href="/A064483/b064483.txt">Table of n, a(n) for n = 1..10000</a> (first 1000 terms from Harry J. Smith)

%e 12 is in the sequence because 144 +/- 37 = 181 and 107 which are both primes.

%e k=30 is a term: 30^2 = 900, prime(30) = 113, 900+113 = 1013 and 900-113 = 787, both primes.

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

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

%o (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

%Y Intersection of A064711 and A064712. - _Zak Seidov_, Oct 12 2014

%K easy,nonn

%O 1,1

%A _Robert G. Wilson v_ and _Jason Earls_, Oct 05 2001