A023201 Primes p such that p + 6 is also prime. (Lesser of a pair of sexy primes.)

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

Offset

1,1

Links

T. D. Noe, Table of n, a(n) for n = 1..10000

Hermann Prossinger, Silvia Boschetti, Tomáš Hladký, Daniel Říha, Jan Slavík, Martin Stachoň, and Jakub Binter, Personality Traits in 12 Countries Defined by the 'Big Five' are Found to Have a Culture Dependency: Implications for Modeling Citizens' Personalities, Human Interaction Emerging Tech. (IHIET 2025) Vol 197, 182-192. See p. 189.

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, 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].

Wikipedia, Sexy prime.

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

Adjacent sequences: A023198 A023199 A023200 * A023202 A023203 A023204

Keyword

nonn,easy

Author

David W. Wilson

Status

approved