A074200 - OEIS

%I #24 Feb 28 2019 18:52:20

%S 1,2,12,12720,19440,5516280,5516280,7321991040,363500177040,

%T 2394196081200,3163427380990800,22755817971366480,3788978012188649280,

%U 2918756139031688155200

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

%C Computed by Jack Brennen and Phil Carmody.

%H Walter Nissen, <a href="http://upforthecount.com/math/pdor.html">Calculation without Words : Doric Columns of Primes</a>.

%H C. Rivera, <a href="http://www.primepuzzles.net/puzzles/puzz_181.htm">Puzzle 181</a>

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

%t 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 *)

%o (PARI) isok(m, n) = {for (k = 1, n, if ((m+k) % k, return (0), if (! isprime((m+k)/k), return(0)));); return (1);}

%o a(n) = {m = 1; while(! isok(m, n), m++); m;} \\ _Michel Marcus_, Aug 31 2013

%o (Python)

%o from sympy import isprime, lcm

%o def A074200(n):

%o     a = lcm(range(1,n+1))

%o     m = a

%o     while True:

%o         for k in range(n,0,-1):

%o             if not isprime(m//k+1):

%o                 break

%o         else:

%o             return m

%o         m += a # _Chai Wah Wu_, Feb 27 2019

%Y Cf. A078502, A278500.

%Y One less than A093553.

%K nonn,more

%O 1,2

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

%E Corrected by _Vladeta Jovovic_, Jan 08 2003

%E a(14) from _Jens Kruse Andersen_, Feb 15 2004