cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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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

Views

Author

Robert Price, Jan 13 2016

Keywords

Comments

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

Examples

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

Links

Crossrefs

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

Programs

  • Mathematica
    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 *)

A271392 Integers k such that 3*k!!! + 1 is prime where k!!! is A007661(k).

Original entry on oeis.org

2, 4, 5, 8, 9, 15, 16, 23, 27, 32, 34, 35, 38, 40, 46, 54, 57, 83, 87, 97, 162, 165, 223, 235, 282, 488, 503, 575, 673, 823, 857, 885, 965, 1112, 1401, 2288, 2569, 2788, 3133, 3539, 4070, 4654, 5020, 5613, 6720, 7773, 11256, 18023, 22196
Offset: 1

Views

Author

Altug Alkan, Apr 06 2016

Keywords

Comments

Corresponding primes are 7, 13, 31, 241, 487, 87481, 174721, 289027201, 21427701121, ...

Examples

			4 is a term because 3*4!!! + 1 = 13 is prime.

Crossrefs

Cf. A007661, A037083, A084438, A217647, A215779, A271396.

Programs

  • PARI
    is(k) = ispseudoprime(3*prod(i=0, (k-2)\3, k-3*i) + 1); \\ Jinyuan Wang, Jun 09 2021

Extensions

a(47) from Jinyuan Wang, Jun 09 2021
a(48)-a(49) from Michael S. Branicky, Aug 10 2024

A271396 Integers k such that 3*k!!! - 1 is prime where k!!! is A007661(k).

Original entry on oeis.org

0, 1, 2, 4, 5, 6, 7, 8, 10, 17, 25, 28, 31, 37, 38, 39, 46, 47, 49, 55, 67, 82, 85, 94, 98, 115, 120, 129, 167, 214, 216, 267, 293, 580, 732, 857, 993, 1012, 1069, 1308, 1430, 2366, 2974, 4017, 4870, 9034, 9061, 9752, 10657, 13847, 25390
Offset: 1

Views

Author

Altug Alkan, Apr 06 2016

Keywords

Comments

Corresponding primes are 2, 2, 5, 11, 29, 53, 83, 239, 839, 628319, 1825823999, 51123071999, ...

Examples

			4 is a term because 3*4!!! - 1 = 11 is prime.

Crossrefs

Cf. A007661, A037083, A084438, A217647, A215779, A271392.

Programs

  • Mathematica
    Select[Range[0,5000],PrimeQ[3Times@@Range[#,1,-3]-1]&] (* The program generates the first 45 terms of the sequence. *) (* Harvey P. Dale, Mar 29 2025 *)
  • PARI
    is(k) = ispseudoprime(3*prod(i=0, (k-2)\3, k-3*i) - 1); \\ Jinyuan Wang, Jun 09 2021

Extensions

a(46)-a(50) from Jinyuan Wang, Jun 09 2021
a(51) from Michael S. Branicky, Aug 09 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

Views

Author

Robert Price, Jul 07 2017

Keywords

Comments

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

Examples

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

Links

Crossrefs

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

Programs

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

Extensions

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

Views

Author

Robert Price, Jun 01 2017

Keywords

Comments

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

Examples

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

Links

Crossrefs

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

Programs

  • Mathematica
    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

Views

Author

Robert Price, Jun 02 2017

Keywords

Comments

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

Examples

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

Links

Crossrefs

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

Programs

  • Mathematica
    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

Views

Author

Robert Price, Jun 03 2017

Keywords

Comments

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

Examples

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

Links

Crossrefs

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

Programs

  • Mathematica
    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

Views

Author

Robert Price, Jun 05 2017

Keywords

Comments

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

Examples

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

Links

Crossrefs

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

Programs

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

A288154 Numbers k such that k!6 + 9 is prime, where k!6 is the sextuple factorial number (A085158 ).

Original entry on oeis.org

2, 4, 14, 28, 34, 46, 50, 52, 86, 100, 106, 140, 166, 170, 208, 242, 338, 344, 412, 1360, 2024, 2948, 3650, 5608, 5744, 7618, 8410, 8834, 11872, 12514, 13636, 18742, 20846, 29750, 31312
Offset: 1

Views

Author

Robert Price, Jun 05 2017

Keywords

Comments

Corresponding primes are: 11, 13, 233, 394249, 13404169, 24663654409, 311607296009, ...
a(36) > 50000.
Terms > 50 correspond to probable primes.

Examples

			14!6 + 9 = 14*8*2 + 9 = 233 is prime, so 14 is in the sequence.

Links

Crossrefs

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

Programs

  • Mathematica
    MultiFactorial[n_, k_] := If[n < 1, 1, n*MultiFactorial[n - k, k]];
Select[Range[0, 50000], PrimeQ[MultiFactorial[#, 6] + 9] &]

A288155 Numbers k such that k!6 + 12 is prime, where k!6 is the sextuple factorial number (A085158 ).

Original entry on oeis.org

0, 1, 5, 7, 11, 13, 17, 19, 23, 25, 41, 67, 71, 101, 109, 151, 163, 181, 233, 241, 265, 355, 433, 563, 767, 997, 1465, 1681, 1861, 1913, 2411, 2539, 2777, 13433, 22355, 30895, 44605
Offset: 1

Views

Author

Robert Price, Jun 05 2017

Keywords

Comments

Corresponding primes are: 13, 13, 17, 19, 67, 103, 947, 1741, 21517, 43237, 894930587, ...
a(37) > 50000.
Terms > 41 correspond to probable primes.

Examples

			11!6 + 12 = 11*5 + 12 = 67 is prime, so 11 is in the sequence.

Links

Crossrefs

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

Programs

  • Mathematica
    MultiFactorial[n_, k_] := If[n < 1, 1, n*MultiFactorial[n - k, k]];
Select[Range[0, 50000], PrimeQ[MultiFactorial[#, 6] + 12] &]
Select[Range[0, 45000], PrimeQ[Times @@ Range[#, 1, -6] + 12] &] (* Harvey P. Dale, Jul 09 2020 *)
Previous Showing 21-30 of 59 results. Next

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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