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A022004
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Initial members of prime triples (p, p+2, p+6).
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78
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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
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OFFSET
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1,1
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COMMENTS
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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
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LINKS
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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
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MAPLE
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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
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MATHEMATICA
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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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PROG
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(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
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CROSSREFS
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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
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KEYWORD
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nonn,easy
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AUTHOR
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Warut Roonguthai
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STATUS
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approved
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