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A064219 a(1) = 1; a(n) > 0; for each k from 1 to n, k divides a(n) or a(n)+1 and a(n) is the least such integer.

%I A064219 #21 Jun 21 2023 08:03:06
%S A064219 1,1,2,3,15,24,35,119,504,720,2519,2519,41040,83160,83160,196559,
%T A064219 524160,524160,3160079,3160079,3160079,3160079,68468400,68468400,
%U A064219 68468400,68468400,4724319600,4724319600,26702675999,26702675999
%N A064219 a(1) = 1; a(n) > 0; for each k from 1 to n, k divides a(n) or a(n)+1 and a(n) is the least such integer.
%H A064219 Chai Wah Wu, <a href="/A064219/b064219.txt">Table of n, a(n) for n = 1..112</a>
%H A064219 Sean A. Irvine, <a href="https://github.com/archmageirvine/joeis/blob/master/src/irvine/oeis/a064/A064219.java">Java program</a> (github)
%e A064219 a(5)=15 because (2 divides a(5)+1) and (3 divides a(5)) and (4 divides a(5)+1) and (5 divides a(5)).
%o A064219 (PARI) { a=1; for (n=1, 100, if (a%n && (a+1)%n, until (b, b=1; a++; for (k=1, n, if (a%k && (a+1)%k, b=0; break)))); write("b064219.txt", n, " ", a) ) } \\ _Harry J. Smith_, Sep 10 2009
%o A064219 (Python)
%o A064219 from math import lcm
%o A064219 from itertools import product
%o A064219 from sympy.ntheory.modular import solve_congruence
%o A064219 def A064219(n):
%o A064219     if n == 1: return 1
%o A064219     alist, blist, c, klist = [], [], 1, list(range(n,1,-1))
%o A064219     while klist:
%o A064219         k = klist.pop(0)
%o A064219         if not c%k:
%o A064219             blist.append(k)
%o A064219         else:
%o A064219             c = lcm(c,k)
%o A064219             alist.append(k)
%o A064219             for m in klist.copy():
%o A064219                 if not k%m:
%o A064219                    klist.remove(m)
%o A064219     for d in product([0,1],repeat=len(alist)):
%o A064219         x = solve_congruence(*list(zip(d,alist)))
%o A064219         if x is not None:
%o A064219             y = x[0]
%o A064219             if y > 1:
%o A064219                 for b in blist:
%o A064219                     if y%b > 1:
%o A064219                         break
%o A064219                 else:
%o A064219                     if y < c:
%o A064219                         c = y
%o A064219     return int(c-1) # _Chai Wah Wu_, Jun 19 2023
%K A064219 easy,nonn
%O A064219 1,3
%A A064219 _Don Reble_, Sep 21 2001