A105411 Primes p = prime(k) such that both p+2 and prime(k+4)-2 are prime numbers.
3, 17, 29, 59, 227, 269, 617, 1031, 1277, 1289, 1301, 1607, 1667, 1697, 2087, 2129, 2309, 2711, 2789, 3257, 3527, 3539, 3557, 3917, 4019, 4241, 4517, 4637, 4787, 5477, 5501, 5639, 6551, 7307, 8819, 8837, 8999, 9011, 10037, 10067, 10271, 10499, 12041
Offset: 1
Keywords
Examples
prime(7) = 17, and both prime(7)+2 = 19 and prime(7+4)-2 = 29 are primes, so 17 is in the sequence.
Links
- Amiram Eldar, Table of n, a(n) for n = 1..10000
Programs
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Magma
[NthPrime(n): n in [1..1500] | IsPrime(NthPrime(n)+2) and IsPrime(NthPrime(n+4)-2)]; // Vincenzo Librandi, Sep 14 2015
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Mathematica
For[n = 1, n < 500, n++, If[PrimeQ[Prime[n] + 2],If[PrimeQ[Prime[n + 4] - 2], Print[Prime[n]]]]] (* Stefan Steinerberger, Feb 07 2006 *) Select[Partition[Prime[Range[1500]],5,1],AllTrue[{#[[1]]+2,#[[5]]-2},PrimeQ]&][[All,1]] (* Harvey P. Dale, Oct 28 2022 *)
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PARI
pnpk(n, m=4, k=2) = { local(x, v1, v2); for(x=1, n, v1 = prime(x)+ k; v2 = prime(x+m)-k; if(isprime(v1)&isprime(v2), print1(prime(x), ", ") ) ) ;} \\ corrected by Michel Marcus, Sep 14 2015 -
PARI
lista(pmax) = {my(k = 1, p = primes(5)); forprime(p1 = p[#p], pmax, k++; p[#p] = p1; if(p[2]- p[1] == 2 && p[5] - p[4] == 2, print1(p[1], ", ")); for(i = 1, #p-1, p[i] = p[i+1]));} \\ Amiram Eldar, Oct 04 2024
Formula
a(n) = prime(A105410(n)-1). - Amiram Eldar, Oct 04 2024
Comments