A123910 -id:A123910 - cp's OEIS frontend

A259359 Numbers n such that n!!-8 is prime.

5, 7, 9, 19, 41, 43, 83, 89, 91, 143, 299, 307, 341, 381, 585, 995, 1019, 1027, 2043, 4301, 6275, 11157, 11621, 12315, 17505, 24771, 30535, 38635

Offset: 1

Robert Price, Jun 24 2015

Corresponding primes are 7, 97, 937, 654729067, 13113070457687988603440617, ... .

a(29) > 50000.

Joe McLean, Interesting Sources of Probable Primes

Cf. A006882, A007749, A094144, A123910, A258616.

Mathematica
```
Select[Range[5,1000],PrimeQ[#!!-8]&]
```

A261344 Numbers n such that n!3 - 3^8 is prime, where n!3 = n!!! is a triple factorial number (A007661).

Original entry on oeis.org

16, 17, 20, 25, 26, 35, 37, 47, 88, 94, 125, 127, 134, 326, 328, 368, 398, 425, 698, 700, 734, 1303, 1427, 2011, 2542, 2699, 3938, 4214, 5137, 6314, 8669, 9041, 12494, 13520, 14609, 23732, 41399, 43867, 49471

Offset: 1

Robert Price, Nov 18 2015

n=5 and n=8 produce values (-6551 and -6481) whose absolute value is a prime.
Corresponding primes are: 51679, 202879, 4182239, 608601439, 2504895839, ...
a(40) > 50000.
Terms > 26 correspond to probable primes.

			16!3 - 3^8 = 16*13*10*7*4*1 - 6561 = 51679 is prime, so 16 is in the sequence.

Henri & Renaud Lifchitz, PRP Records. Search for n!3-6561.
Joe McLean, Interesting Sources of Probable Primes
OpenPFGW Project, Primality Tester

Cf. A007661, A037082, A084438, A123910, A242994.

MultiFactorial[n_, k_] := If[n < 1, 1, If[n < k + 1, n, n*MultiFactorial[n - k, k]]];
Select[Range[0, 50000], PrimeQ[MultiFactorial[#, 3] - 3^8] &]
Select[Range[14,800],PrimeQ[Times@@Range[#,1,-3]-6561]&] (* The program generates the first 21 terms of the sequence. To generate more, increase the Range constant. *) (* Harvey P. Dale, Apr 27 2022 *)

for(n=1, 1e3, if(ispseudoprime(prod(i=0, floor((n-1)/3), n-3*i) - 3^8), print1(n, ", "))) \\ Altug Alkan, Nov 18 2015

A265378 Numbers n such that n!3 + 3^9 is prime, where n!3 = n!!! is a triple factorial number (A007661).

Original entry on oeis.org

4, 8, 10, 11, 14, 17, 20, 22, 29, 32, 44, 56, 61, 173, 202, 211, 215, 241, 388, 410, 416, 569, 583, 680, 823, 964, 1271, 1732, 2309, 2335, 2404, 2765, 3019, 3047, 4670, 5209, 6320, 6817, 7531, 9923, 11243, 14912, 17969, 21193, 28940

Offset: 1

Robert Price, Dec 07 2015

Corresponding primes are: 19687, 19763, 19963, 20563, 32003, 229123, 4208483, 24364003, 72642189283, ...
a(46) > 50000.
Terms > 61 correspond to probable primes.

			11!3 + 3^9 = 11*8*5*2 + 19683 = 20563 is prime, so 11 is in the sequence.

Henri & Renaud Lifchitz, PRP Records. Search for n!3+19683.
Joe McLean, Interesting Sources of Probable Primes
OpenPFGW Project, Primality Tester

Cf. A007661, A037082, A084438, A123910, A242994, A261145, A265200.

MultiFactorial[n_, k_] := If[n < 1, 1, If[n < k + 1, n, n*MultiFactorial[n - k, k]]];
Select[Range[0, 50000], PrimeQ[MultiFactorial[#, 3] + 3^9] &]

tf(n) = prod(i=0, (n-1)\3, n-3*i);
for(n=1, 1e4, if(ispseudoprime(tf(n) + 3^9), print1(n , ", "))) \\ Altug Alkan, Dec 07 2015

A267029 Numbers n such that n!!! - 3^9 is prime, where n!3 = n!!! is a triple factorial number (A007661).

Original entry on oeis.org

16, 17, 34, 38, 49, 62, 74, 97, 125, 137, 146, 178, 188, 235, 664, 863, 916, 1988, 2059, 2837, 5353, 5489, 7483, 9344, 12631, 13796, 17122, 23134, 30409, 33077

Offset: 1

Robert Price, Jan 09 2016

Corresponding primes are 38557, 189757, 17961239276317, 3091650738156317, ... .

a(31) > 50000.

			16!3 - 3^9 = 16*13*10*7*4*1 - 19683 = 58240 - 19683 = 38557 is prime, so 16 is in the sequence.

Henri & Renaud Lifchitz, PRP Records. Search for n!3-19683.
Joe McLean, Interesting Sources of Probable Primes

Cf. A006882, A007749, A094144, A123910, A258452, A258616, A262772, A261145, A265201.

MultiFactorial[n_, k_] := If[n < 1, 1, If[n < k + 1, n, n*MultiFactorial[n - k, k]]];
Select[Range[15, 50000], PrimeQ[MultiFactorial[#, 3] - 3^9] &]
Select[Range[12,33100],PrimeQ[Times@@Range[#,1,-3]-19683]&] (* Harvey P. Dale, Jan 25 2021 *)

A267382 Numbers n such that n!3 - 3^7 is prime, where n!3 = n!!! is a triple factorial number (A007661).

Original entry on oeis.org

13, 14, 16, 19, 22, 23, 26, 38, 64, 104, 137, 203, 296, 346, 347, 379, 481, 568, 899, 1162, 1603, 2614, 5698, 5846, 9253, 9565, 9848, 10406, 16051, 18377, 23110, 26026, 26120, 28994

Offset: 1

Robert Price, Jan 13 2016

Corresponding primes are: 1453, 10133, 56053, 1104373, 24342133, 2504900213, 3091650738173813, ... .
a(35) > 50000.
Terms > 26 correspond to probable primes.

			13!3 - 3^7 = 13*10*7*4 - 2187 = 1453 is prime, so 13 is in the sequence.

Henri & Renaud Lifchitz, PRP Records. Search for n!3-2187.
Joe McLean, Interesting Sources of Probable Primes
OpenPFGW Project, Primality Tester

Cf. A007661, A037082, A084438, A123910, A242994, A261145, A265200.

MultiFactorial[n_, k_] := If[n < 1, 1, If[n < k + 1, n, n*MultiFactorial[n - k, k]]];
Select[Range[13, 50000], PrimeQ[MultiFactorial[#, 3] - 3^7] &]
Select[Range[12,6000],PrimeQ[Times@@Range[#,1,-3]-2187]&] (* The program generates the first 24 terms of the sequence. *) (* Harvey P. Dale, Aug 14 2024 *)

A279646 Numbers k such that k!6 - 3 is prime, where k!6 is the sextuple factorial number (A085158).

Original entry on oeis.org

5, 6, 8, 10, 68, 82, 92, 98, 118, 286, 796, 878, 1360, 1502, 1516, 1568, 1646, 3628, 3716, 4048, 7982, 12776, 18070, 20594, 29902, 39632, 52988, 53864, 55610, 67448, 85402, 89762

Offset: 1

Robert Price, Jul 07 2017

Corresponding primes are: 2, 3, 13, 37, 73569236156415997, ...
a(33) > 10^5.
Terms > 10 correspond to probable primes.

			10!6 - 3 = 10*4 - 3 = 37 is prime, so 10 is in the sequence.

Henri & Renaud Lifchitz, PRP Records. Search for n!6-3.
Joe McLean, Interesting Sources of Probable Primes
OpenPFGW Project, Primality Tester

Cf. A007661, A037082, A084438, A123910, A242994.

MultiFactorial[n_, k_] := If[n < 1, 1, n*MultiFactorial[n - k, k]];
Select[Range[4, 50000], PrimeQ[MultiFactorial[#, 6] - 3] &]

a(27)-a(32) from Robert Price, Aug 03 2018

A287844 Numbers k such that k!6 + 3 is prime, where k!6 is the sextuple factorial number (A085158 ).

Original entry on oeis.org

2, 4, 8, 10, 14, 16, 20, 22, 26, 34, 70, 164, 346, 398, 902, 938, 1426, 1682, 1928, 3596, 3796, 15058, 25654, 37330

Offset: 1

Robert Price, Jun 01 2017

Corresponding primes are: 5, 7, 19, 43, 227, 643, 4483, 14083, 116483, 13404163, ...
a(25) > 50000.
Terms > 34 correspond to probable primes.

			10!6 + 3 = 10*4 + 3 = 43 is prime, so 10 is in the sequence.

Henri & Renaud Lifchitz, PRP Records. Search for n!6+3.
Joe McLean, Interesting Sources of Probable Primes
OpenPFGW Project, Primality Tester

Cf. A007661, A037082, A084438, A123910, A242994.

MultiFactorial[n_, k_] := If[n < 1, 1, n*MultiFactorial[n - k, k]];
Select[Range[0, 50000], PrimeQ[MultiFactorial[#, 6] + 3] &]
Select[Range[3800],PrimeQ[Times@@Range[#,1,-6]+3]&] (* The program generates the first 21 terms of the sequence. *) (* Harvey P. Dale, May 23 2025 *)

A287914 Numbers k such that k!6 + 4 is prime, where k!6 is the sextuple factorial number (A085158 ).

Original entry on oeis.org

1, 3, 7, 9, 11, 15, 19, 27, 35, 59, 71, 75, 95, 109, 153, 155, 169, 189, 277, 355, 383, 405, 455, 625, 843, 853, 879, 1389, 1423, 1515, 1871, 2059, 2677, 3095, 4473, 5691, 5927, 8149, 10789, 12171, 14683, 26383, 34227, 40945

Offset: 1

Robert Price, Jun 02 2017

Corresponding primes are: 5, 7, 11, 31, 59, 409, 1733, 229639, 21827579, ...
a(45) > 50000.
Terms > 35 correspond to probable primes.

			11!6 + 4 = 11*5 + 4 = 59 is prime, so 11 is in the sequence.

Henri & Renaud Lifchitz, PRP Records. Search for n!6+4.
Joe McLean, Interesting Sources of Probable Primes
OpenPFGW Project, Primality Tester

Cf. A007661, A037082, A084438, A123910, A242994.

MultiFactorial[n_, k_] := If[n < 1, 1, n*MultiFactorial[n - k, k]];
Select[Range[0, 50000], PrimeQ[MultiFactorial[#, 6] + 4] &]

A287956 Numbers k such that k!6 + 6 is prime, where k!6 is the sextuple factorial number (A085158 ).

Original entry on oeis.org

1, 5, 7, 11, 13, 17, 37, 43, 55, 107, 139, 149, 157, 211, 223, 343, 373, 409, 523, 12049, 16457, 17143, 17543, 18391, 25829, 25945, 31307, 34601, 41687

Offset: 1

Robert Price, Jun 03 2017

Corresponding primes are: 7, 11, 13, 61, 97, 941, 49579081, 2131900231, 5745471106381, ...
a(43) > 50000.
Terms > 35 correspond to probable primes.

			11!6 + 6 = 11*5 + 6 = 61 is prime, so 11 is in the sequence.

Henri & Renaud Lifchitz, PRP Records. Search for n!6+6.
Joe McLean, Interesting Sources of Probable Primes
OpenPFGW Project, Primality Tester

Cf. A007661, A037082, A084438, A123910, A242994.

MultiFactorial[n_, k_] := If[n < 1, 1, n*MultiFactorial[n - k, k]];
Select[Range[0, 50000], PrimeQ[MultiFactorial[#, 6] + 6] &]

A288152 Numbers k such that k!6 + 8 is prime, where k!6 is the sextuple factorial number (A085158 ).

Original entry on oeis.org

3, 5, 21, 29, 41, 65, 243, 305, 389, 509, 819, 1653, 7493, 8613, 8619, 10257, 11829, 12977, 15651, 24341, 29367, 31629, 40173

Offset: 1

Robert Price, Jun 05 2017

Corresponding primes are: 11, 13, 8513, 623653, 894930583, 8549258359016383, ...
a(24) > 50000.
Terms > 41 correspond to probable primes.

			21!6 + 8 = 21*15*9*3 + 8 = 8513 is prime, so 21 is in the sequence.

Henri & Renaud Lifchitz, PRP Records. Search for n!6+8.
Joe McLean, Interesting Sources of Probable Primes
OpenPFGW Project, Primality Tester

Cf. A007661, A037082, A084438, A123910, A242994.

MultiFactorial[n_, k_] := If[n < 1, 1, n*MultiFactorial[n - k, k]];
Select[Range[0, 50000], PrimeQ[MultiFactorial[#, 6] + 8] &]

cp's OEIS Frontend

A259359 Numbers n such that n!!-8 is prime.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

A261344 Numbers n such that n!3 - 3^8 is prime, where n!3 = n!!! is a triple factorial number (A007661).

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

PARI

A265378 Numbers n such that n!3 + 3^9 is prime, where n!3 = n!!! is a triple factorial number (A007661).

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

PARI

A267029 Numbers n such that n!!! - 3^9 is prime, where n!3 = n!!! is a triple factorial number (A007661).

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

A267382 Numbers n such that n!3 - 3^7 is prime, where n!3 = n!!! is a triple factorial number (A007661).

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

A279646 Numbers k such that k!6 - 3 is prime, where k!6 is the sextuple factorial number (A085158).

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

Extensions

A287844 Numbers k such that k!6 + 3 is prime, where k!6 is the sextuple factorial number (A085158 ).

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

A287914 Numbers k such that k!6 + 4 is prime, where k!6 is the sextuple factorial number (A085158 ).

Views

Author

Keywords

Comments

Examples

Links