This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A182126 #38 Aug 17 2025 21:12:08 %S A182126 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 A182126 24,12,24,125,72,60,16,120,24,48,72,40,60,72,16,120,24,24,12,168,65, %U A182126 64,12,24,60,16,120,96,72,72,16,48,40,12,120,29,72,12,24,252 %N A182126 a(n) = prime(n)*prime(n+1) mod prime(n+2). %C A182126 Conjecture: for x>10^9, the most frequent value in a(n), n=0...x, has form 120*k. %C A182126 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 A182126 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 A182126 Reinhard Zumkeller, <a href="/A182126/b182126.txt">Table of n, a(n) for n = 1..10000</a> %e A182126 (2*3) mod 5 = 1, (3*5) mod 7 = 1, (5*7) mod 11 = 2, (7*11) mod 13 = 12. %p A182126 P:= [seq(ithprime(i),i=1..102)]: %p A182126 seq(P[i]*P[i+1] mod P[i+2], i=1..100); # _Robert Israel_, Jun 19 2017 %t A182126 Mod[#[[1]]#[[2]],#[[3]]]&/@Partition[Prime[Range[70]],3,1] (* _Harvey P. Dale_, Sep 30 2015 *) %o A182126 (Haskell) %o A182126 a182126 n = a182126_list !! (n-1) %o A182126 a182126_list = zipWith3 (\p p' p'' -> mod (p * p') p'') %o A182126 a000040_list (tail a000040_list) (drop 2 a000040_list) %o A182126 -- _Reinhard Zumkeller_, Apr 23 2012 %o A182126 (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 A182126 (Magma) [NthPrime(n)*NthPrime(n+1) mod NthPrime(n+2): n in [1..70]]; // _Vincenzo Librandi_, Jun 20 2017 %Y A182126 Cf. A000040, A022461, A022462. %K A182126 nonn,easy %O A182126 1,3 %A A182126 _Alex Ratushnyak_, Apr 13 2012