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A073830 a(n) = 4*((n-1)! + 1) + n (mod n*(n + 2)). 5
0, 2, 0, 8, 0, 10, 56, 12, 22, 14, 0, 16, 182, 18, 34, 20, 0, 22, 380, 24, 46, 26, 552, 28, 29, 30, 58, 32, 0, 34, 992, 36, 37, 38, 74, 40, 1406, 42, 82, 44, 0, 46, 1892, 48, 94, 50, 2256, 52, 53, 54, 106, 56, 2862, 58, 59, 60, 118, 62, 0, 64, 3782, 66, 67, 68, 134, 70 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Amiram Eldar, Table of n, a(n) for n = 1..10000

Chris Caldwell, Twin Prime

P. A. Clement, Congruences for sets of primes, The American Mathematical Monthly, Vol. 56, No. 1 (1949), pp. 23-25.

PlanetMath, Clement’s theorem on twin primes.

FORMULA

a(n) = A073829(n) mod A005563(n).

For n > 1: a(n) = 0 iff (n, n+2) are twin primes (Clement, 1949).

From Bernard Schott, Nov 16 2021: (Start)

If p is an odd prime, and p+2 is composite, then a(p) = p*(p+1).

If m is composite, and m+2 is prime, then a(m) = 2*(m+2).

If n even >= 4, a(n) = n + 4.

If p prime >= 5, a(p^2) = p^2 + 4. (End)

MAPLE

A073830 := proc(n)

    4*((n-1)!+1)+n ;

    modp(%, n*(n+2)) ;

end proc:

seq(A073830(n), n=1..60) ; # R. J. Mathar, Feb 21 2017

MATHEMATICA

a[n_] := Mod[4 ((n - 1)! + 1) + n, n (n + 2)]; Array[a, 66] (* Jean-François Alcover, Feb 22 2018 *)

PROG

(MAGMA) [(4*(Factorial(n-1)+1)+n) mod (n^2+2*n): n in [1..70]]; // Vincenzo Librandi, May 04 2014

CROSSREFS

Cf. A001359, A005563, A006512, A073831, A073832.

Sequence in context: A200489 A011124 A011250 * A213272 A053205 A167029

Adjacent sequences:  A073827 A073828 A073829 * A073831 A073832 A073833

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller, Aug 12 2002

STATUS

approved

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Last modified December 7 20:40 EST 2021. Contains 349589 sequences. (Running on oeis4.)