A070858 Smallest prime == 1 mod L, where L = LCM of 1 to n.

2, 3, 7, 13, 61, 61, 421, 2521, 2521, 2521, 55441, 55441, 4324321, 4324321, 4324321, 4324321, 85765681, 85765681, 232792561, 232792561, 232792561, 232792561, 10708457761, 10708457761, 26771144401, 26771144401, 401567166001, 401567166001, 18632716502401, 18632716502401

Offset: 1

Author

Amarnath Murthy, May 16 2002

Keywords

• nonn

Comments

Beginning with 3, smallest prime p = a(n) such that p + k is divisible by k + 1 for each k = 1, 2, ..., n. For example: 61 --> 62, 63, 64, 65 and 66 are divisible respectively by 2, 3, 4, 5 and 6. - Robin Garcia, Jul 23 2012

Links

• Amiram Eldar, Table of n, a(n) for n = 1..1000 (terms 1..200 from R. J. Mathar)

Crossrefs

Cf. A060357, A075059, A003418, A070844 to A070856, A035091.

Programs

Maple

A070858 := proc(n)
    local l,p;
    l := ilcm(seq(i,i=1..n)) ;
    for p from 1 by l do
        if isprime(p) then
            return p;
        end if;
    end do:
end proc; # R. J. Mathar, Jun 25 2013

Mathematica

a[n_] := Module[{m = 1, lcm = LCM @@ Range[n]}, While[!PrimeQ[m], m += lcm]; m]; Array[a, 30] (* Amiram Eldar, Mar 15 2025 *)

PARI

a(n)=my(L=lcm(vector(n,i,i)),k=1);while(!ispseudoprime(k+=L),); k \\ Charles R Greathouse IV, Jun 25 2013

Extensions

More terms from Sascha Kurz, Feb 02 2003