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A023201 Primes p such that p + 6 is also prime. (Lesser of a pair of sexy primes.) 116
5, 7, 11, 13, 17, 23, 31, 37, 41, 47, 53, 61, 67, 73, 83, 97, 101, 103, 107, 131, 151, 157, 167, 173, 191, 193, 223, 227, 233, 251, 257, 263, 271, 277, 307, 311, 331, 347, 353, 367, 373, 383, 433, 443, 457, 461, 503, 541, 557, 563, 571, 587, 593, 601, 607, 613, 641, 647 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
LINKS
Eric Weisstein's World of Mathematics, Sexy Primes. [The definition in this webpage is unsatisfactory, because it defines a "sexy prime" as a pair of primes.- N. J. A. Sloane, Mar 07 2021].
FORMULA
From M. F. Hasler, Jan 02 2020: (Start)
a(n) = A046117(n) - 6 = A087695(n) - 3.
A023201 = { p = A000040(k) | A000040(k+1) = p+6 or A000040(k+2) = p+6 } = A031924 U A007529. (End)
MAPLE
A023201 := proc(n)
option remember;
if n = 1 then
5;
else
for a from procname(n-1)+2 by 2 do
if isprime(a) and isprime(a+6) then
return a;
end if;
end do:
end if;
end proc: # R. J. Mathar, May 28 2013
MATHEMATICA
Select[Range[10^2], PrimeQ[ # ]&&PrimeQ[ #+6] &] (* Vladimir Joseph Stephan Orlovsky, Apr 29 2008 *)
Select[Prime[Range[120]], PrimeQ[#+6]&] (* Harvey P. Dale, Mar 20 2018 *)
PROG
(Magma) [n: n in [0..40000] | IsPrime(n) and IsPrime(n+6)] // Vincenzo Librandi, Aug 04 2010
(Haskell)
a023201 n = a023201_list !! (n-1)
a023201_list = filter ((== 1) . a010051 . (+ 6)) a000040_list
-- Reinhard Zumkeller, Feb 25 2013
(PARI) is(n)=isprime(n+6)&&isprime(n) \\ Charles R Greathouse IV, Mar 20 2013
CROSSREFS
A031924 (primes starting a gap of 6) and A007529 together give this (A023201).
Cf. A046117 (a(n)+6), A087695 (a(n)+3), A098428, A000040, A010051, A006489 (subsequence).
Sequence in context: A040146 A243593 A015914 * A106059 A102386 A348936
KEYWORD
nonn,easy
AUTHOR
STATUS
approved

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Last modified March 19 04:58 EDT 2024. Contains 370952 sequences. (Running on oeis4.)