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 A033932 Least positive m such that n! + m is prime. 23
 1, 1, 1, 1, 5, 7, 7, 11, 23, 17, 11, 1, 29, 67, 19, 43, 23, 31, 37, 89, 29, 31, 31, 97, 131, 41, 59, 1, 67, 223, 107, 127, 79, 37, 97, 61, 131, 1, 43, 97, 53, 1, 97, 71, 47, 239, 101, 233, 53, 83, 61, 271, 53, 71, 223, 71, 149, 107, 283, 293, 271, 769, 131, 271 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS Conjecture: No term is a composite number. a(n) is a prime > 3*prime(k), where k is such that prime(k) < n <= prime(k+1). - Amarnath Murthy, Apr 07 2004 Terms after n = 2000 in the b-file correspond to Fermat and Lucas PRP. - Phillip Poplin, Oct 12 2019 LINKS Phillip Poplin, Table of n, a(n) for n = 0..4000 (first 501 terms from T. D. Noe, then up to n=2000 from Hans Havermann) Antonín Čejchan, Michal Křížek, and Lawrence Somer, On Remarkable Properties of Primes Near Factorials and Primorials, Journal of Integer Sequences, Vol. 25 (2022), Article 22.1.4. Index entries for sequences related to factorial numbers FORMULA a(n) = A151800(n!) - n!. - Max Alekseyev, Jul 23 2014 MAPLE a:= n-> (f-> nextprime(f)-f)(n!): seq(a(n), n=0..70); # Alois P. Heinz, Feb 22 2023 MATHEMATICA a[n_] := (an = 1; While[ !PrimeQ[n! + an], an++]; an); Table[a[n], {n, 0, 63}] (* Jean-François Alcover, Dec 05 2012 *) NextPrime[#]-#&/@(Range[0, 70]!) (* Harvey P. Dale, May 18 2014 *) PROG (PARI) for(n=0, 70, k=1; while(!isprime(n!+k), k++); print1(k, ", ")) (PARI) a(n) = nextprime(n!+1) - n!; \\ Michel Marcus, Dec 25 2020 (Python) from sympy import factorial, nextprime def a(n): fn = factorial(n); return nextprime(fn) - fn print([a(n) for n in range(64)]) # Michael S. Branicky, May 22 2022 CROSSREFS Cf. A000142, A002981, A033933, A037151, A037153, A056752, A053714, A151800. Sequence in context: A159482 A231935 A216835 * A144186 A246458 A153979 Adjacent sequences: A033929 A033930 A033931 * A033933 A033934 A033935 KEYWORD nice,nonn AUTHOR Jeff Burch EXTENSIONS More terms from Jud McCranie a(21) onwards from Wouter Meeussen Better description from Rick L. Shepherd, Nov 06 2002 STATUS approved

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Last modified February 21 04:08 EST 2024. Contains 370219 sequences. (Running on oeis4.)