A033932 -id:A033932 - cp's OEIS frontend

A120621 Least positive k such that !n + k is prime, where !n is left factorial.

2, 1, 1, 1, 1, 3, 3, 3, 9, 3, 7, 9, 7, 13, 49, 27, 9, 37, 19, 33, 7, 93, 103, 9, 73, 27, 13, 27, 165, 49, 39, 93, 97, 27, 37, 39, 135, 7, 193, 249, 39, 103, 13, 33, 213, 129, 33, 13, 39, 115, 187, 19, 7, 387, 19, 489, 303, 63, 33, 235, 297, 495, 657, 465, 235, 193, 369, 129

Offset: 0

Jason Earls, Aug 17 2006

Amiram Eldar, Table of n, a(n) for n = 0..1000

Cf. A003422, A033932 (with n! instead of !n).

a[n_] := Module[{k = 1, lf = Sum[i!, {i, 0, n - 1}]}, While[!PrimeQ[lf + k], k++]; k]; Array[a, 100, 0] (* Amiram Eldar, Dec 24 2019 *)

A269485 Least k > 0 such that n! + k^2 is prime.

Original entry on oeis.org

1, 1, 1, 1, 7, 11, 7, 13, 17, 31, 13, 1, 47, 17, 19, 19, 23, 73, 43, 29, 47, 31, 43, 29, 31, 37, 167, 1, 29, 43, 79, 229, 89, 71, 137, 37, 53, 1, 79, 131, 137, 1, 71, 83, 89, 89, 53, 97, 53, 101, 59, 173, 79, 71, 353, 191, 103, 523, 229, 191, 103, 401, 67, 257

Offset: 0

Jean-Marc Rebert, Feb 28 2016

nonn

a(n) = A033932(n) = 1 for n in A002981.

			a(4) = 7, because 4! + 7^2 = 73 is prime and for 0 < i < 7, 4! + i^2 is not prime.

Jean-Marc Rebert, Table of n, a(n) for n = 0..500

Cf. A002981, A033932, A038202.

Table[SelectFirst[Range@ 10000, PrimeQ[n! + #^2] &], {n, 120}]
(* Version 10, or *)
Table[k = 1; While[! PrimeQ[n! + k^2], k++]; k, {n, 120}] (* Michael De Vlieger, Feb 28 2016 *)

a(n) = {my(k=1); while (!isprime(n! + k^2), k++); k;} \\ Michel Marcus, Feb 29 2016

A257886 Least positive m such that floor(n! / (2*(floor(n/2)!))) + m is prime.

Original entry on oeis.org

2, 1, 2, 1, 1, 1, 1, 13, 1, 1, 29, 1, 1, 37, 29, 17, 31, 71, 71, 37, 23, 1, 37, 1, 41, 41, 31, 31, 59, 31, 41, 41, 41, 41, 41, 37, 41, 193, 83, 41, 53, 67, 149, 97, 59, 73, 113, 107, 137, 59, 137, 67, 101, 83, 73, 101, 241, 71, 73, 79, 83, 227, 199, 223, 127, 83, 83, 181, 227, 149, 103, 1, 587, 179, 229, 167, 127, 163, 109, 83

Offset: 1

David Morales Marciel, May 11 2015

nonn

Conjecture: No term is composite (similar conjecture to A033932 for a different expression).

			n = 1, floor(1! / (2*(floor(1/2)!)))=0, m = 2, and 0+2=2 is prime.
n = 2, floor(2! / (2*(floor(2/2)!)))=1, m = 1, and 1+1=2 is prime.
...
n = 15, floor(15! / (2*(floor(15/2)!)))=129729600, m = 29, and 129729600+29 = 129729629 is prime.

David Morales Marciel, About Fortunate numbers and other similar expressions

Cf. A033932.

lpm[n_]:=Module[{c=Floor[n!/(2Floor[n/2]!)]},NextPrime[c]-c]; Array[lpm,80] (* Harvey P. Dale, May 15 2018 *)

from sympy import factorial, nextprime
[(nextprime(int(factorial(n)/(2*factorial(n//2)))))-int(factorial(n)/(2*factorial(n//2))) for n in range(1,10**5)]

Edited. Wolfdieter Lang, Jun 08 2015

cp's OEIS Frontend

A120621 Least positive k such that !n + k is prime, where !n is left factorial.

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

A269485 Least k > 0 such that n! + k^2 is prime.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

PARI

A257886 Least positive m such that floor(n! / (2*(floor(n/2)!))) + m is prime.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

Python

Extensions