A182126 - OEIS

%I #35 Sep 08 2022 08:45:54

%S 1,1,2,12,7,12,1,2,16,11,40,12,24,7,13,16,48,40,12,48,40,60,15,48,12,

%T 24,12,24,125,72,60,16,120,24,48,72,40,60,72,16,120,24,24,12,168,65,

%U 64,12,24,60,16,120,96,72,72,16,48,40,12,120,29,72,12,24,252

%N a(n) = prime(n)*prime(n+1) mod prime(n+2).

%C Conjecture: for x>10^9, the most frequent value in a(n), n=0...x, has form 120*k.

%C Let b = prime(n+2) - prime(n) and c = prime(n+2) - prime(n+1). Conjecture: for n > 61, a(n) = b*c. This holds up to n = 9 * 10^16. - _Charles R Greathouse IV_, May 11 2012

%C With b and c as above, a(n) = b*c if and only if b*c < prime(n+2). Cramér's conjecture implies this is true for all sufficiently large n. - _Robert Israel_, Jun 19 2017

%H Reinhard Zumkeller, <a href="/A182126/b182126.txt">Table of n, a(n) for n = 1..10000</a>

%e (2*3) mod 5 = 1, (3*5) mod 7 = 1, (5*7) mod 11 = 2, (7*11) mod 13 = 12.

%p P:= [seq(ithprime(i),i=1..102)]:

%p seq(P[i]*P[i+1] mod P[i+2], i=1..100); # _Robert Israel_, Jun 19 2017

%t Mod[#[[1]]#[[2]],#[[3]]]&/@Partition[Prime[Range[70]],3,1] (* _Harvey P. Dale_, Sep 30 2015 *)

%o (Haskell)

%o a182126 n = a182126_list !! (n-1)

%o a182126_list = zipWith3 (\p p' p'' -> mod (p * p') p'')

%o                   a000040_list (tail a000040_list) (drop 2 a000040_list)

%o -- _Reinhard Zumkeller_, Apr 23 2012

%o (PARI) p=2;q=3;forprime(r=5,1e3,print1(p*q%r", ");p=q;q=r) \\ _Charles R Greathouse IV_, May 11 2012

%o (Magma) [NthPrime(n)*NthPrime(n+1) mod NthPrime(n+2): n in [1..70]]; // _Vincenzo Librandi_, Jun 20 2017

%Y Cf. A000040, A022461, A022462.

%K nonn,easy

%O 1,3

%A Alex Ratushnyak, Apr 13 2012