A022004 Initial members of prime triples (p, p+2, p+6).
5, 11, 17, 41, 101, 107, 191, 227, 311, 347, 461, 641, 821, 857, 881, 1091, 1277, 1301, 1427, 1481, 1487, 1607, 1871, 1997, 2081, 2237, 2267, 2657, 2687, 3251, 3461, 3527, 3671, 3917, 4001, 4127, 4517, 4637, 4787, 4931, 4967, 5231, 5477
Offset: 1
Links
- Matt C. Anderson Table of n, a(n) for n = 1..10000 (terms 1..1000 from T. D. Noe)
- T. Forbes and Norman Luhn, Prime k-tuplets
- R. J. Mathar, Table of Prime Gap Constellations (2013,2024), 275 pages (no not print...)
- Thomas R. Nicely, Enumeration of the prime triples (q,q+2,q+6) to 1e16.
- P. Pollack, Analytic and Combinatorial Number Theory, Course Notes, p. 132, ex. 3.4.3. [Broken link?]
- P. Pollack, Analytic and Combinatorial Number Theory, Course Notes, p. 132, ex. 3.4.3.
- Maxie D. Schmidt, New Congruences and Finite Difference Equations for Generalized Factorial Functions, arXiv:1701.04741 [math.CO], 2017.
- Eric Weisstein's World of Mathematics, Prime Triplet
- Index entries for primes, gaps between
Crossrefs
Programs
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Magma
[ p: p in PrimesUpTo(10000) | IsPrime(p+2) and IsPrime(p+6) ] // Vincenzo Librandi, Nov 19 2010
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Maple
A022004 := proc(n) if n= 1 then 5; else for a from procname(n-1)+2 by 2 do if isprime(a) and isprime(a+2) and isprime(a+6) then return a; end if; end do: end if; end proc: # R. J. Mathar, Jul 11 2012
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Mathematica
Select[Prime[Range[1000]], PrimeQ[#+2] && PrimeQ[#+6]&] (* Vladimir Joseph Stephan Orlovsky, Mar 30 2011 *) Transpose[Select[Partition[Prime[Range[1000]],3,1],Differences[#]=={2,4}&]][[1]] (* Harvey P. Dale, Dec 24 2011 *)
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PARI
is(n)=isprime(n)&&isprime(n+2)&&isprime(n+6) \\ Charles R Greathouse IV, Jul 01 2013
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Python
from sympy import primerange def aupto(limit): p, q, alst = 2, 3, [] for r in primerange(5, limit+7): if p+2 == q and p+6 == r: alst.append(p) p, q = q, r return alst print(aupto(5477)) # Michael S. Branicky, May 11 2021
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