A377318 Numbers k such that prime(k), prime(k)+6, prime(k)+12, and prime(k)+18 are primes.
3, 5, 13, 18, 54, 110, 116, 182, 234, 252, 271, 284, 351, 387, 464, 541, 551, 682, 709, 717, 741, 821, 829, 1171, 1417, 1448, 1510, 1594, 1711, 1726, 1842, 1853, 2009, 2086, 2209, 2297, 2408, 2600, 2680, 2876, 2924, 2930, 3253, 3303, 3437, 3977, 4384, 4431
Offset: 1
Keywords
Examples
5 is in this sequence because: prime(5) = 11 and 11+6=17, 11+12=23, and 11+18=29 are all primes.
Links
- Harvey P. Dale, Table of n, a(n) for n = 1..1000
Programs
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Mathematica
Select[Range[1, PrimePi[50000]], PrimeQ[Prime[#] + 6] && PrimeQ[Prime[#] + 12] && PrimeQ[Prime[#] + 18] &] Select[Range[4500],AllTrue[Prime[#]+{0,6,12,18},PrimeQ]&] (* Harvey P. Dale, Jun 17 2025 *) -
PARI
for(k=1, primepi(50000), p = prime(k); if(isprime(p+6) && isprime(p+12) && isprime(p+18), print(k)))
Formula
a(n) = pi(A023271(n)).