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 A022004 Initial members of prime triples (p, p+2, p+6). 78
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Solutions of the equation n' + (n+2)' + (n+6)' = 3, where n' is the arithmetic derivative of n. - Paolo P. Lava, Nov 09 2012 Subsequence of A001359. - R. J. Mathar, Feb 10 2013 All terms are congruent to 5 (mod 6). - Matt C. Anderson, May 22 2015 Intersection of A001359 and A023201. - Zak Seidov, Mar 12 2016 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 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 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 # Alternative select(n->isprime(n) and isprime(n+2) and isprime(n+6), [\$2..10^4]); # Paolo P. Lava, Apr 23 2018 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 *) PROG (Magma) [ p: p in PrimesUpTo(10000) | IsPrime(p+2) and IsPrime(p+6) ] // Vincenzo Librandi, Nov 19 2010 (PARI) is(n)=isprime(n)&&isprime(n+2)&&isprime(n+6) \\ Charles R Greathouse IV, Jul 01 2013 (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 CROSSREFS Cf. A073648, A098412. Cf. A001359 and A023201. - Zak Seidov, Mar 12 2016 Subsequence of A007529. Sequence in context: A136091 A184968 A341357 * A339503 A172454 A162001 Adjacent sequences: A022001 A022002 A022003 * A022005 A022006 A022007 KEYWORD nonn,easy AUTHOR STATUS approved

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Last modified March 31 15:31 EDT 2023. Contains 361668 sequences. (Running on oeis4.)