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A033933 Least nonnegative m such that n! - m is prime.

%I A033933 #64 Jan 15 2022 11:59:41
%S A033933 0,1,1,7,1,1,31,13,11,13,1,23,1,47,53,59,41,101,31,31,73,89,73,149,37,
%T A033933 43,101,31,1,61,1,1,193,113,127,97,1,73,83,131,79,109,109,53,89,79,
%U A033933 103,59,97,179,67,59,127,61,461,277,109,137,139,71,71,101,359,127,317,191,251,103,97,751,163,373,199,167,157,491,317
%N A033933 Least nonnegative m such that n! - m is prime.
%C A033933 Conjecture: for n >= 3, a(n) is 1 or a prime. - _Amarnath Murthy_, Mar 19 2002
%C A033933 a(n) is not divisible by any prime <= n. If a(n) > 1 is composite, then a(n) > n^2. There are no entries up to n = 2000 with a(n) > n^2, and there may be none. - _Robert Israel_, Jul 20 2014
%H A033933 Hans Havermann, <a href="/A033933/b033933.txt">Table of n, a(n) for n = 2..2000</a> (terms 2..500 from T. D. Noe)
%H A033933 <a href="/index/Fa#factorial">Index entries for sequences related to factorial numbers</a>
%p A033933 0, seq(n! - prevprime(n!), n=3..100); # _Robert Israel_, Jul 15 2014
%t A033933 p[n_] := Module[{nf = n!}, nf - NextPrime[nf, -1]]; Join[{0}, Table[p[n], {n, 3, 70}]] (* _Harvey P. Dale_, Jul 07 2012 *)
%o A033933 (PARI) for(n=2,70, k=0; while(!isprime(n!-k), k++); print1(k,","))
%o A033933 (PARI) vector(66, t, my(n=t+1, f=n!); f-precprime(f)) \\ _Joerg Arndt_, Jul 19 2014
%o A033933 (Sage)
%o A033933 def A033933(n):
%o A033933     if n < 3: return 0
%o A033933     f = factorial(n)
%o A033933     return f - previous_prime(f)
%o A033933 [A033933(n) for n in (2..78)] # _Peter Luschny_, Jul 20 2014
%Y A033933 Cf. A002982, A006990, A033932, A056752, A053714.
%K A033933 nonn,nice
%O A033933 2,4
%A A033933 _Jeff Burch_
%E A033933 More terms from _Jud McCranie_
%E A033933 a(21) onwards from _Wouter Meeussen_
%E A033933 Corrected by _Rick L. Shepherd_, Nov 06 2002