A092969 -id:A092969 - cp's OEIS frontend

A092970 Smallest prime of the form n!/k + 1. k < = n, or 0 if no such prime exists.

2, 2, 3, 7, 31, 181, 1009, 13441, 45361, 453601, 3991681, 39916801, 566092801, 10897286401, 130767436801, 2988969984001, 25406244864001, 0, 8109673360588801, 304112751022080001, 2688996956405760001

Offset: 1

Amarnath Murthy, Mar 26 2004

nonn

			a(10) = 453601 = 10!/8 + 1, as 10!/10 + 1 and 10!/9 + 1 are both composite.

Cf. A092968, A092969, A092068.

Table[SelectFirst[Reverse[n!/Range[n]+1],PrimeQ],{n,30}]/.(Missing[ "NotFound"] -> 0) (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jan 15 2019 *)

a(n)=for (i=1,n,if(isprime(n!/(n-i+1)+1),return((n!/(n-i+1)+1))))

Corrected and extended by Mohammed Bouayoun (bouyao(AT)wanadoo.fr), Mar 26 2004

A093520 Numbers n such that there exists no k with 0 < k < n for which n!/k + 1 is a prime.

Original entry on oeis.org

1, 18, 51, 53, 84, 95, 100, 104, 106, 143, 178, 180, 181, 188, 202, 203, 211, 214, 217, 222, 227, 232, 237, 239, 244, 250, 258, 272, 281, 284, 300, 303, 313, 315, 317, 323, 326, 342, 358, 364, 370, 374, 386, 387, 396, 401, 409, 413, 422, 423, 429, 438, 440

Offset: 1

Robert G. Wilson v, Mar 29 2004

nonn

Essentially the same as A092068. - R. J. Mathar, Sep 05 2008

Cf. A092969.

f[n_] := Block[{k = 1}, While[ !PrimeQ[n!/k + 1], k++ ]; If[k < n, n!/k + 1, 0]]; Do[ If[ f[n] == 0, Print[n]], {n, 440}]
Join[{1},Select[Range[500],NoneTrue[#!/Range[#]+1,PrimeQ]&]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jul 14 2018 *)

A206762 a(n) is the least number from 1,2,...,n-1, such that n!/a(n)+1 is prime, and a(n)=0, if such number does not exist.

Original entry on oeis.org

1, 1, 2, 2, 3, 2, 2, 5, 6, 1, 8, 2, 5, 7, 2, 3, 0, 5, 8, 4, 16, 3, 8, 4, 10, 1, 13, 8, 2, 19, 4, 11, 11, 7, 3, 1, 12, 13, 4, 1, 24, 2, 8, 5, 9, 25, 16, 2, 12, 0, 26, 0, 17, 22, 44, 22, 37, 7, 48, 4, 37, 18, 7, 39, 16, 19, 7, 15, 19, 36, 30, 1, 14, 15, 16, 1

Offset: 2

Vladimir Shevelev, Feb 12 2012

nonn

The sequence of primes n!/a(n)+1, when a(n)>0, is increasing.

Cf. A089136, A092265, A092965, A092969, A092970.

Table[s = Select[Range[n - 1], PrimeQ[n!/# + 1] &, 1]; If[s == {}, 0, s[[1]]], {n, 2, 100}] (* T. D. Noe, Feb 13 2012 *)

cp's OEIS Frontend

A092970 Smallest prime of the form n!/k + 1. k < = n, or 0 if no such prime exists.

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A093520 Numbers n such that there exists no k with 0 < k < n for which n!/k + 1 is a prime.

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A206762 a(n) is the least number from 1,2,...,n-1, such that n!/a(n)+1 is prime, and a(n)=0, if such number does not exist.

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