A245458 a(n) = ((prime(n)-2)!+2) mod prime(n)# (cf. A002110).

1, 3, 8, 122, 212, 6932, 450452, 9189182, 193993802, 2677114442, 116454478142, 5415133233512, 51945166943672, 1521251317636052, 562558737261811292, 1229779565176982822, 130356633908760178922, 19227603501542126390702, 4456958491657464897364262

Offset: 1

Author

Vladimir Shevelev, Jul 22 2014

Keywords

• nonn

Comments

Smallest positive residue modulo p_1*...*p_n (cf. A002110) of (p_n-2)!+2, where p_n=prime(n).

See comment in A245460.

Links

• Jens Kruse Andersen, Table of n, a(n) for n = 1..100
• V. Shevelev, Theorems on twin primes-dual case, arXiv:0912.4006 (Sections 10,11,14-18)

Crossrefs

Cf. A002110, A245457, A244570, A244571, A244572.

Programs

Mathematica

a[n_] := Mod[(Prime[n]-2)! + 2, Product[Prime[i], {i, 1, n}]];
Array[a, 19] (* Jean-François Alcover, Dec 15 2018 *)

PARI

a(n) = ((prime(n)-2)!+2) % prod(i=1, n, prime(i)) \\ Jens Kruse Andersen, Jul 22 2014

Extensions

More terms and simpler definition from Jens Kruse Andersen, Jul 22 2014