login
A064483
Numbers k such that k^2 + prime(k) and k^2 - prime(k) are both primes.
1
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
1,1
COMMENTS
All terms are multiples of 6. - Jon E. Schoenfield, Apr 13 2024
LINKS
Zak Seidov, Table of n, a(n) for n = 1..10000 (first 1000 terms from Harry J. Smith)
EXAMPLE
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.
MATHEMATICA
Select[ Range[10^4], PrimeQ[ #^2 + Prime[ # ]] && PrimeQ[ #^2 - Prime[ # ]] &]
PROG
(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
CROSSREFS
Intersection of A064711 and A064712. - Zak Seidov, Oct 12 2014
Sequence in context: A086830 A084699 A323441 * A375718 A365277 A322181
KEYWORD
easy,nonn
AUTHOR
STATUS
approved