A075758 -id:A075758 - cp's OEIS frontend

A231901 Least k > n such that k!/n! + 1 is a prime, or 0 if no such k exists.

1, 2, 4, 4, 6, 6, 11, 9, 11, 10, 20, 12, 15, 15, 16, 16, 18, 18, 23, 21, 22, 22, 40, 25, 27, 31, 28, 28, 37, 30, 42, 38, 34, 36, 42, 36, 110, 39, 43, 40, 42, 42, 56, 46, 50, 46, 55, 65, 51, 51, 53, 52, 55, 55, 73, 58, 58, 58, 60, 60, 63, 63, 177, 68, 70, 66, 82, 72

Offset: 0

Alex Ratushnyak, Nov 15 2013

nonn

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Cf. A002981, A035093, A057217, A075757, A075758, A231549.

Table[k = n + 1; While[! PrimeQ[k!/n! + 1], k++]; k, {n, 100}] (* T. D. Noe, Nov 18 2013 *)

a(n) = {my(m = n+1); while(! isprime(m!/n! +1), m++); m;} \\ Michel Marcus, Mar 07 2014; corrected Jun 13 2022

A231549 Least k>0 such that k!*n!+1 is a prime, or 0 if no such k exists.

Original entry on oeis.org

1, 1, 1, 4, 2, 8, 3, 3, 3, 4, 1, 2, 3, 5, 8, 4, 10, 2, 11, 9, 5, 5, 7, 3, 14, 18, 1, 40, 24, 5, 5, 18, 8, 20, 2, 49, 1, 3, 5, 28, 1, 17, 38, 27, 11, 16, 10, 3, 24, 270, 2, 45, 2, 15, 175, 64, 17, 6, 4, 3, 8, 18, 13, 17, 65, 32, 12, 7, 72, 13, 21, 33, 1, 24, 36, 76, 1

Offset: 1

Alex Ratushnyak, Nov 15 2013

nonn

Indices of 1's: A002981.

Cf. A002981, A035093, A057217, A075757, A075758, A231901.

Table[k = 1; While[! PrimeQ[k!*n! + 1], k++]; k, {n, 100}] (* T. D. Noe, Nov 18 2013 *)

A108097 Numbers k such that there is no j <= k with k!+j!-1 prime.

Original entry on oeis.org

1, 13, 19, 30, 32, 48, 54, 62, 63, 64, 68, 74, 75, 78, 90, 92, 93, 106, 109, 111, 112, 115, 117, 123, 128, 129, 131, 133, 135, 138, 144, 146, 156, 158, 159, 161, 162, 168, 170, 174, 175, 196, 197, 205, 211, 213, 217, 218, 219, 220, 230, 234

Offset: 1

Ralf Stephan, Jun 01 2005

nonn

Cf. A075758.

Select[Range[250],NoneTrue[(#!-1)+Range[#]!,PrimeQ]&] (* The program uses the NoneTrue function from Mathematica version 10 *) (* Harvey P. Dale, Mar 28 2015 *)

A108098 Numbers m such that there is no k <= 2*m for which m! + k! - 1 is prime.

Original entry on oeis.org

48, 63, 68, 74, 111, 129, 135, 161, 168, 174, 197, 236, 240, 243, 273, 279, 282, 285, 309, 322, 335, 347, 360, 393, 407, 419, 431, 437, 439, 440, 455, 460, 461, 483, 491, 494, 497, 512, 517, 522, 526, 532, 544, 567, 591, 614, 625, 650, 662, 663, 681, 687

Offset: 1

Ralf Stephan, Jun 01 2005

nonn

For numbers m <= 320 that are not in the sequence, there exists an integer k <= 2*m such that m! + k! - 1 is a certified prime. For m > 320 the values of m! + k! - 1 are only probable primes. - Ryan Propper, Sep 02 2005

Cf. A075758.

Do[l = Range[1, 2*n]; If[Length[Select[l, PrimeQ[n! + #! - 1]&]] == 0, Print[n]], {n, 1, 729}] (* Ryan Propper, Sep 02 2005 *)
Select[Range[700],NoneTrue[Table[#!+k!-1,{k,2#}],PrimeQ]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Aug 24 2019 *)

a(13)-a(52) from Ryan Propper, Sep 02 2005

Name edited by Jon E. Schoenfield, Nov 18 2018

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A231901 Least k > n such that k!/n! + 1 is a prime, or 0 if no such k exists.

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A231549 Least k>0 such that k!*n!+1 is a prime, or 0 if no such k exists.

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A108097 Numbers k such that there is no j <= k with k!+j!-1 prime.

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A108098 Numbers m such that there is no k <= 2*m for which m! + k! - 1 is prime.

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