A074200 a(n) = m, the smallest number such that (m+k)/k is prime for k=1, 2, ..., n.

1, 2, 12, 12720, 19440, 5516280, 5516280, 7321991040, 363500177040, 2394196081200, 3163427380990800, 22755817971366480, 3788978012188649280, 2918756139031688155200

Offset: 1

Author

Jean-Christophe Colin (jc-colin(AT)wanadoo.fr), Sep 17 2002, May 10 2010

Keywords

• nonn
• more

Comments

Computed by Jack Brennen and Phil Carmody.

Examples

			(12+k)/k is prime for k = 1,2,3. 12 is the smallest such number so a(3) = 12.
		

Links

• Walter Nissen, Calculation without Words : Doric Columns of Primes.
• C. Rivera, Puzzle 181

Crossrefs

Cf. A078502, A278500.

One less than A093553.

Programs

Mathematica

a[1] = 1; a[n_] := a[n] = For[dm = LCM @@ Range[n]; m = Quotient[a[n - 1], dm]*dm, True, m = m + dm, If[AllTrue[Range[n], PrimeQ[(m + #)/#] &], Return[m]]]; Table[an = a[n]; Print["a(", n, ") = ", an]; an, {n, 1, 10}] (* Jean-François Alcover, Dec 01 2016 *)

PARI

isok(m, n) = {for (k = 1, n, if ((m+k) % k, return (0), if (! isprime((m+k)/k), return(0)));); return (1);}
a(n) = {m = 1; while(! isok(m, n), m++); m;} \\ Michel Marcus, Aug 31 2013

Python

from sympy import isprime, lcm
def A074200(n):
    a = lcm(range(1,n+1))
    m = a
    while True:
        for k in range(n,0,-1):
            if not isprime(m//k+1):
                break
        else:
            return m
        m += a # Chai Wah Wu, Feb 27 2019

Extensions

Corrected by Vladeta Jovovic, Jan 08 2003

a(14) from Jens Kruse Andersen, Feb 15 2004