A139063 -id:A139063 - cp's OEIS frontend

A139071 Numbers k for which (10+k!)/10 is prime.

5, 6, 11, 12, 15, 23, 26, 37, 45, 108, 112, 129, 137, 148, 172, 248, 760, 807, 975, 1398, 5231, 8765, 24182

Offset: 1

Artur Jasinski, Apr 07 2008

nonn

Primes of the form (10+k!)/10 see A139070.

a(24) > 25000. - Robert Price, Nov 08 2016

Cf. A082672, A089085, A089130, A117141, A007749, A139056, A139057, A139058, A139059, A139060, A139061, A139061, A139062, A139063, A139064, A139065, A139066, A020458, A139068, A137390, A139070, A139071, A139072.

Cf. n!/m-1 is a prime: A002982, A082671, A139056, A139199-A139205; n!/m+1 is a prime: A002981, A082672, A089085, A139061, A139058, A139063, A139065, A151913, A137390, A139071 (1<=m<=10).

a = {}; Do[If[PrimeQ[(n! + 10)/10], AppendTo[a, n]], {n, 1, 500}]; a

for(k=5,1e3,if(ispseudoprime(k!/10+1),print1(k", "))) \\ Charles R Greathouse IV, Jul 15 2011

More terms from Serge Batalov, Feb 18 2015

a(22)-a(23) from Robert Price, Nov 08 2016

A082671 Numbers n such that (n!-2)/2 is a prime.

Original entry on oeis.org

3, 4, 5, 6, 9, 31, 41, 373, 589, 812, 989, 1115, 1488, 1864, 1918, 4412, 4686, 5821, 13830

Offset: 1

Cino Hilliard, May 18 2003

			(4!-2)/2 = 11 is a prime.

Cf. n!/m-1 is a prime: A002982, A082671, A139056, A139199, A139200, A139201, A139202, A139203, A139204, A139205; n!/m+1 is a prime: A002981, A082672, A089085, A139061, A139058, A139063, A139065, A151913, A137390, A139071

[n: n in [1..600]| IsPrime((Factorial(n)-2) div 2)]; // Vincenzo Librandi, Feb 18 2015

Select[Range[0, 14000], PrimeQ[(#! - 2) / 2] &] (* Vincenzo Librandi, Feb 18 2015 *)

xfactpk(n,k=2) = { for(x=2,n, y = (x!-k)/k; if(isprime(y),print1(x", ")) ) }

More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 03 2008

Edited by T. D. Noe, Oct 30 2008

A139199 Numbers k such that (k!-4)/4 is prime.

Original entry on oeis.org

4, 5, 6, 7, 8, 10, 15, 18, 23, 157, 165, 183, 184, 362, 611, 908, 2940, 6875, 9446, 16041

Offset: 1

Artur Jasinski, Apr 11 2008

Numbers k such that (k!-m)/m is prime:
for m=1 see A002982
for m=2 prime or pseudoprime see A082671
for m=3 see A139056
for m=4 see A139199
for m=5 see A139200
for m=6 see A139201
for m=7 see A139202
for m=8 see A139203
for m=9 see A139204
for m=10 see A139205
a(17) > 2000 - Ray G. Opao, Sep 30 2008
a(21) > 25000 - Robert Price, Sep 25 2016

Cf. A139189, A139190, A139191, A139192, A139193, A139194, A139195, A139196, A139197, A139198.

Cf. n!/m-1 is a prime: A002982, A082671, A139056, A139199-A139205; n!/m+1 is a prime: A002981, A082672, A089085, A139061, A139058, A139063, A139065, A151913, A137390, A139071 (1<=m<=10).

a = {}; Do[If[PrimeQ[(n! - 4)/4], Print[a]; AppendTo[a, n]], {n, 1, 184}]; a (*Artur Jasinski*)

is(n)=n>3 && isprime(n!/4-1) \\ Charles R Greathouse IV, Apr 29 2015

a(15)-a(16) from Ray G. Opao, Sep 30 2008
a(17) from Serge Batalov, Feb 18 2015
a(18)-a(20) from Robert Price, Sep 25 2016

A139205 Numbers k such that (k!-10)/10 is prime.

Original entry on oeis.org

5, 6, 7, 11, 13, 17, 28, 81, 87, 433, 640, 647, 798, 1026, 1216, 1277, 3825, 6684

Offset: 1

Artur Jasinski, Apr 11 2008

a(19) > 25000. - Robert Price, Dec 23 2016

Cf. A139189, A139190, A139191, A139192, A139193, A139194, A139195, A139196, A139197, A139198.

Cf. n!/m-1 is a prime: A002982, A082671, A139056, A139199-A139205; n!/m+1 is a prime: A002981, A082672, A089085, A139061, A139058, A139063, A139065, A151913, A137390, A139071 (1<=m<=10).

a = {}; Do[If[PrimeQ[(n! - 10)/10], Print[a]; AppendTo[a, n]], {n, 1, 300}]; a (*Artur Jasinski*)
Select[Range[700],PrimeQ[(#!-10)/10]&] (* Harvey P. Dale, Feb 15 2015 *)

One additional term (a(12)) from Harvey P. Dale, Feb 15 2015
More terms from Serge Batalov, Feb 18 2015
a(18) from Robert Price, Dec 23 2016

A151913 Numbers n for which (8+n!)/8 is prime.

Original entry on oeis.org

7, 9, 10, 12, 14, 20, 23, 24, 29, 44, 108, 2049, 3072, 4862, 8807, 15089

Offset: 1

Artur Jasinski, Apr 07 2008

nonn

a(17) > 25000. - Robert Price, Dec 20 2016

For primes of the form (8+k!!)/8 see A139066.
Cf. A089130, A117141, A139035, A139057, A139059, A139060, A139062, A139064, A139067.
Cf. n!/m-1 is a prime: A002982, A082671, A139056, A139199-A139205; n!/m+1 is a prime: A002981, A082672, A089085, A139061, A139058, A139063, A139065, A151913, A137390, A139071 (1<=m<=10).

a = {}; Do[If[PrimeQ[(n! + 8)/8], AppendTo[a, n]], {n, 1, 500}]; a

is(n)=n>6 && isprime((8+n!)/8) \\ Charles R Greathouse IV, Apr 29 2016

Definition corrected Feb 24 2010
More terms from Serge Batalov, Feb 18 2015
a(15)-a(16) from Robert Price, Dec 20 2016

A076680 Numbers k such that 4*k! + 1 is prime.

Original entry on oeis.org

0, 1, 4, 7, 8, 9, 13, 16, 28, 54, 86, 129, 190, 351, 466, 697, 938, 1510, 2748, 2878, 3396, 4057, 4384, 5534, 7069, 10364

Offset: 1

Phillip L. Poplin (plpoplin(AT)bellsouth.net), Oct 25 2002

a(25) > 6311. - Jinyuan Wang, Feb 06 2020

			k = 7 is a term because 4*7! + 1 = 20161 is prime.

Factor Database, Factors of the numbers 4z!+1

Cf. m*n!-1 is a prime: A076133, A076134, A099350, A099351, A180627-A180631.
Cf. m*n!+1 is a prime: A051915, A076679-A076683, A178488, A180626, A126896.
Cf. n!/m-1 is a prime: A002982, A082671, A139056, A139199-A139205.
Cf. n!/m+1 is a prime: A002981, A082672, A089085, A139061, A139058, A139063, A139065, A151913, A137390, A139071.

Select[Range[5000],PrimeQ[4#!+1]&] (* Harvey P. Dale, Mar 23 2011 *)

is(k) = ispseudoprime(4*k!+1); \\ Jinyuan Wang, Feb 06 2020

Corrected (added missed terms 2748, 2878) by Serge Batalov, Feb 24 2015
a(24) from Jinyuan Wang, Feb 06 2020
a(25)-a(26) from Michael S. Branicky, Jul 04 2024

A139060 Primes of the form (4+k!)/4.

Original entry on oeis.org

7, 31, 181, 1556755201, 12772735542927360001, 3877802510832746496000001, 65782709233423382541804503040000001, 203978820811974433586402817399028973568000000001

Offset: 1

Artur Jasinski, Apr 07 2008

nonn

For numbers k for which (4+k!)/4 is prime see A139061.

Amiram Eldar, Table of n, a(n) for n = 1..15

Cf. A007749, A020458, A082672, A089085, A089130, A117141, A139056, A139057, A139058, A139059, A139061, A139062, A139063, A139064, A139065, A139066, A139151.

a = {}; Do[If[PrimeQ[(n! + 4)/4], AppendTo[a, (n! + 4)/4]], {n, 1, 50}]; a
Select[(4+Range[100]!)/4,PrimeQ] (* Harvey P. Dale, Oct 05 2016 *)

for(k=4,1e3,if(ispseudoprime(t=k!/4+1),print1(t", "))) \\ Charles R Greathouse IV, Jul 15 2011

a(n) = A139151(A139061(n)). - Amiram Eldar, Oct 13 2024

A139062 Primes of the form (6+k!)/6.

Original entry on oeis.org

2, 5, 604801, 6652801, 1037836801, 14529715201, 59281238016001, 8515157028618240001

Offset: 1

Artur Jasinski, Apr 07 2008

nonn

For numbers k for which (6+k!)/6 is prime see A139063.

Amiram Eldar, Table of n, a(n) for n = 1..17

Cf. A020458, A082672, A089085, A089130, A117141, A007749, A139056, A139057, A139058, A139059, A139060, A139061, A139063, A139064, A139065, A139066, A139153.

a = {}; Do[If[PrimeQ[(n! + 6)/6], AppendTo[a, (n! + 6)/6]], {n, 1, 50}]; a

for(k=3,1e3,if(ispseudoprime(t=k!/6+1),print1(t", "))) \\ Charles R Greathouse IV, Jul 15 2011

a(n) = A139153(A139063(n)). - Amiram Eldar, Oct 14 2024

A139064 Primes of the form (7+k!)/7.

Original entry on oeis.org

5702401, 186810624001, 2988969984001, 2215887149047283712000001, 1476163995198020704238093048217600000001, 19811874077955690819705574245769915192271839538955347505831613562880000000000001

Offset: 1

Artur Jasinski, Apr 07 2008

nonn

For numbers k for which (7+k!)/7 is prime see A139065.

Amiram Eldar, Table of n, a(n) for n = 1..12

Cf. A020458, A082672, A089085, A089130, A117141, A007749, A139056, A139057, A139058, A139059, A139060, A139061, A139062, A139063, A139065, A139066, A139154.

a = {}; Do[If[PrimeQ[(n! + 7)/7], AppendTo[a, (n! + 7)/7]], {n, 1, 50}]; a

for(k=7,1e3,if(ispseudoprime(t=k!/7+1),print1(t", "))) \\ Charles R Greathouse IV, Jul 15 2011

a(n) = A139154(A139065(n)). - Amiram Eldar, Oct 14 2024

A139200 Numbers k such that (k!-5)/5 is prime.

Original entry on oeis.org

5, 11, 12, 16, 36, 41, 42, 47, 127, 136, 356, 829, 1863, 2065, 2702, 4509, 7498

Offset: 1

Artur Jasinski, Apr 11 2008

a(16) > 3000. - Ray G. Opao, Oct 05 2008

a(18) > 25000. - Robert Price, Nov 20 2016

Cf. A139189, A139190, A139191, A139192, A139193, A139194, A139195, A139196, A139197, A139198.

Cf. n!/m-1 is a prime: A002982, A082671, A139056, A139199-A139205; n!/m+1 is a prime: A002981, A082672, A089085, A139061, A139058, A139063, A139065, A151913, A137390, A139071 (1<=m<=10).

[n: n in [5..500] | IsPrime((Factorial(n)-5) div 5)]; // Vincenzo Librandi, Nov 21 2016

a = {}; Do[If[PrimeQ[(n! - 5)/5], Print[a]; AppendTo[a, n]], {n, 1, 300}]; a (* Artur Jasinski *)

a(13)-a(15) from Ray G. Opao, Oct 05 2008
a(16) from Serge Batalov, Feb 18 2015
a(17) from Robert Price, Nov 20 2016

cp's OEIS Frontend

A139071 Numbers k for which (10+k!)/10 is prime.

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A082671 Numbers n such that (n!-2)/2 is a prime.

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A139199 Numbers k such that (k!-4)/4 is prime.

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A139205 Numbers k such that (k!-10)/10 is prime.

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A151913 Numbers n for which (8+n!)/8 is prime.

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A076680 Numbers k such that 4*k! + 1 is prime.

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A139060 Primes of the form (4+k!)/4.

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A139062 Primes of the form (6+k!)/6.

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