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
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
KEYWORD
nonn
AUTHOR
Reinhard Zumkeller, Aug 12 2002
STATUS
approved