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

%I A074200 #24 Feb 28 2019 18:52:20
%S A074200 1,2,12,12720,19440,5516280,5516280,7321991040,363500177040,
%T A074200 2394196081200,3163427380990800,22755817971366480,3788978012188649280,
%U A074200 2918756139031688155200
%N A074200 a(n) = m, the smallest number such that (m+k)/k is prime for k=1, 2, ..., n.
%C A074200 Computed by Jack Brennen and Phil Carmody.
%H A074200 Walter Nissen, <a href="http://upforthecount.com/math/pdor.html">Calculation without Words : Doric Columns of Primes</a>.
%H A074200 C. Rivera, <a href="http://www.primepuzzles.net/puzzles/puzz_181.htm">Puzzle 181</a>
%e A074200 (12+k)/k is prime for k = 1,2,3. 12 is the smallest such number so a(3) = 12.
%t A074200 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 A074200 (PARI) isok(m, n) = {for (k = 1, n, if ((m+k) % k, return (0), if (! isprime((m+k)/k), return(0)));); return (1);}
%o A074200 a(n) = {m = 1; while(! isok(m, n), m++); m;} \\ _Michel Marcus_, Aug 31 2013
%o A074200 (Python)
%o A074200 from sympy import isprime, lcm
%o A074200 def A074200(n):
%o A074200     a = lcm(range(1,n+1))
%o A074200     m = a
%o A074200     while True:
%o A074200         for k in range(n,0,-1):
%o A074200             if not isprime(m//k+1):
%o A074200                 break
%o A074200         else:
%o A074200             return m
%o A074200         m += a # _Chai Wah Wu_, Feb 27 2019
%Y A074200 Cf. A078502, A278500.
%Y A074200 One less than A093553.
%K A074200 nonn,more
%O A074200 1,2
%A A074200 Jean-Christophe Colin (jc-colin(AT)wanadoo.fr), Sep 17 2002, May 10 2010
%E A074200 Corrected by _Vladeta Jovovic_, Jan 08 2003
%E A074200 a(14) from _Jens Kruse Andersen_, Feb 15 2004