A139189 -id:A139189 - cp's OEIS frontend

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

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

A139191 Natural numbers of the form (prime(n)!-3)/3.

Original entry on oeis.org

1, 39, 1679, 13305599, 2075673599, 118562476031999, 40548366802943999, 8617338912961658879999, 2947253997913233984847871999999, 2740946218059307605908520959999999, 4587917697075448348771993193860300799999999, 11150842204387935702723354017813583888383999999999, 20138421021124611879118377356171332502421503999999999, 86207747170389393547654785051203993323065877463039999999999, 1424961094686675188099337917796466549896781262788937908223999999999999

Offset: 1

Artur Jasinski, Apr 11 2008

nonn

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

Mathematica
```
Table[(Prime[n]! - 3)/3, {n, 2, 20}]
```

a(n)=(A139189(n+1)-2)/3. - R. J. Mathar, May 25 2008

More terms from R. J. Mathar, May 25 2008

A139190 a(n) = (prime(n)!-2)/2.

Original entry on oeis.org

0, 2, 59, 2519, 19958399, 3113510399, 177843714047999, 60822550204415999, 12926008369442488319999, 4420880996869850977271807999999, 4111419327088961408862781439999999, 6881876545613172523157989790790451199999999, 16726263306581903554085031026720375832575999999999, 30207631531686917818677566034256998753632255999999999, 129311620755584090321482177576805989984598816194559999999999, 2137441642030012782149006876694699824845171894183406862335999999999999

Offset: 1

Artur Jasinski, Apr 11 2008

nonn

Alois P. Heinz, Table of n, a(n) for n = 1..85

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

Mathematica
```
Table[(Prime[n]! - 2)/2, {n, 1, 20}]
```

a(n) = (prime(n)!-2)/2 \\ Charles R Greathouse IV, Apr 29 2015

a(n) = (A139189(n)-1)/2. - R. J. Mathar, May 25 2008

More terms from R. J. Mathar, May 25 2008

A139192 a(n) = (prime(n)! - 4)/4.

Original entry on oeis.org

29, 1259, 9979199, 1556755199, 88921857023999, 30411275102207999, 6463004184721244159999, 2210440498434925488635903999999, 2055709663544480704431390719999999, 3440938272806586261578994895395225599999999, 8363131653290951777042515513360187916287999999999, 15103815765843458909338783017128499376816127999999999, 64655810377792045160741088788402994992299408097279999999999, 1068720821015006391074503438347349912422585947091703431167999999999999

Offset: 3

Artur Jasinski, Apr 11 2008

nonn

Vincenzo Librandi, Table of n, a(n) for n = 3..87

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

[(Factorial(NthPrime(n))-4)/4: n in [3..20]]; // Vincenzo Librandi, Jun 02 2017

Mathematica
```
Table[(Prime[n]! - 4)/4, {n, 3, 20}]
```

a(n) = (prime(n)!-4)/4;
lista(nn) = for (n=3, nn, print1(a(n), ", ")); \\ Michel Marcus, Feb 17 2018

a(n) = (A139189(n+2) - 3)/4. - R. J. Mathar, May 25 2008

More terms from R. J. Mathar, May 25 2008

A139193 Natural numbers of the form (prime(n)! - 5)/5.

Original entry on oeis.org

23, 1007, 7983359, 1245404159, 71137485619199, 24329020081766399, 5170403347776995327999, 1768352398747940390908723199999, 1644567730835584563545112575999999

Offset: 1

Artur Jasinski, Apr 11 2008

nonn

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

A039716 := proc(n) factorial(ithprime(n)) ; end: A139193 := proc(n) A039716(n)/5-1 ; end: seq(A139193(n),n=3..14) ; # R. J. Mathar, Sep 18 2009

Mathematica
```
Table[(Prime[n]! - 5)/5, {n, 3, 20}]
```

A139194 Natural numbers of the form (prime(n)!-6)/6.

Original entry on oeis.org

0, 19, 839, 6652799, 1037836799, 59281238015999, 20274183401471999, 4308669456480829439999, 1473626998956616992423935999999, 1370473109029653802954260479999999

Offset: 1

Artur Jasinski, Apr 11 2008

nonn

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

Mathematica
```
Table[(Prime[n]! - 6)/6, {n, 2, 20}]
```

A139195 (prime(n)!-7)/7.

Original entry on oeis.org

719, 5702399, 889574399, 50812489727999, 17377871486975999, 3693145248412139519999, 1263108856248528850649087999999, 1174691236311131831103651839999999, 1966250441603763578045139940225843199999999

Offset: 4

Artur Jasinski, Apr 11 2008

nonn

Not an integer for n < 4.

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

Mathematica
```
Table[(Prime[n]! - 7)/7, {n, 4, 20}]
```

Edited with one more term by Franklin T. Adams-Watters, Apr 09 2009

A139196 a(n) = (prime(n)!-8)/8.

Original entry on oeis.org

14, 629, 4989599, 778377599, 44460928511999, 15205637551103999, 3231502092360622079999, 1105220249217462744317951999999, 1027854831772240352215695359999999, 1720469136403293130789497447697612799999999

Offset: 3

Artur Jasinski, Apr 11 2008

nonn

Cf. A039716, A139189, A139190, A139191, A139192, A139193, A139194, A139195, A139196, A139197, A139198.

Mathematica
```
Table[(Prime[n]! - 8)/8, {n, 3, 20}]
```

a(n) = (A039716(n) - 8)/8. - Elmo R. Oliveira, Jan 20 2023

Edited by Max Alekseyev, Sep 15 2009

A139197 Natural numbers of the form (prime(n)!-9)/9.

Original entry on oeis.org

559, 4435199, 691891199, 39520825343999, 13516122267647999, 2872446304320552959999, 982417999304411328282623999999, 913648739353102535302840319999999

Offset: 1

Artur Jasinski, Apr 11 2008

nonn

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

Table[(Prime[n]! - 9)/9, {n, 4, 20}]
(Prime[Range[4,20]]!-9)/9 (* Harvey P. Dale, Apr 10 2019 *)

cp's OEIS Frontend

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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A139191 Natural numbers of the form (prime(n)!-3)/3.

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A139190 a(n) = (prime(n)!-2)/2.

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A139192 a(n) = (prime(n)! - 4)/4.

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Magma

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A139193 Natural numbers of the form (prime(n)! - 5)/5.

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Maple

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A139194 Natural numbers of the form (prime(n)!-6)/6.

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Mathematica

A139195 (prime(n)!-7)/7.

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A139196 a(n) = (prime(n)!-8)/8.

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