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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A247868 Numbers n such that n!3 + 3^5 is prime, where n!3 = n!!! is a triple factorial number (A007661).

Original entry on oeis.org

7, 10, 11, 22, 23, 25, 44, 46, 47, 50, 53, 55, 89, 122, 214, 410, 427, 526, 539, 575, 1369, 1370, 2291, 4999, 5374, 7202, 7375, 7823, 8921, 9764, 22967, 25507, 44117
Offset: 1

Views

Author

Robert Price, Sep 25 2014

Keywords

Comments

Large terms correspond to probable primes.
a(34) > 50000.

Examples

			10!3+243 = 10*7*4*1+243= 523 is prime, so 10 is in the sequence.

Links

Crossrefs

Cf. A007661, A037082, A084438, A243078.

Programs

  • Mathematica
    MultiFactorial[n_, k_] := If[n < 1, 1, If[n < k + 1, n, n*MultiFactorial[n - k, k]]];
lst={};Do[If[PrimeQ[MultiFactorial[n, 3] + 243], AppendTo[lst, n]], {n, 100}];lst

A249400 Numbers n such that n!3 + 3 is prime, where n!3 = n!!! is a triple factorial number (A007661).

Original entry on oeis.org

2, 4, 5, 7, 8, 10, 11, 13, 14, 16, 19, 20, 26, 28, 29, 32, 41, 56, 61, 77, 100, 169, 181, 205, 338, 347, 955, 1952, 2197, 2428, 2960, 3430, 4618, 7478, 8209, 8422, 9235, 11107, 13481, 18194, 19229, 29854, 46532
Offset: 1

Views

Author

Robert Price, Oct 27 2014

Keywords

Comments

Large terms correspond to probable primes.
a(44) > 50000.

Examples

			11!3+3 = 11*8*5*2+3 = 883 is prime, so 11 is in the sequence.

Links

Crossrefs

Cf. A007661, A037082, A084438, A243078.

Programs

  • Mathematica
    MultiFactorial[n_, k_] := If[n < 1, 1, If[n < k + 1, n, n*MultiFactorial[n - k, k]]];
lst={};Do[If[PrimeQ[MultiFactorial[n, 3] + 3], AppendTo[lst, n]], {n, 100}];lst

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

Views

Author

Robert Price, Nov 18 2015

Keywords

Comments

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.

Examples

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

Links

Crossrefs

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

Programs

  • Mathematica
    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 *)
  • PARI
    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

A264867 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

2, 5, 10, 26, 34, 35, 37, 59, 68, 76, 104, 106, 188, 193, 242, 278, 287, 290, 572, 772, 773, 1304, 2384, 2716, 3715, 4562, 6706, 11489, 11711, 21602, 24295, 24775, 27224, 29935, 37856
Offset: 1

Views

Author

Robert Price, Nov 26 2015

Keywords

Comments

Corresponding primes are 6563, 6571, 6841, 2504908961, 17961239302561, 81359229958561, 664565853958561, ...
Terms > 68 correspond to probable primes.
a(36) > 50000.

Examples

			10!3 + 3^4 = 10*7*4*1 + 6561 = 6841 is prime, so 10 is in the sequence.

Links

Crossrefs

Cf. A007661, A037082, A084438, A243078.

Programs

  • Mathematica
    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[800],PrimeQ[6561+Times@@Range[#,1,-3]]&] (* Harvey P. Dale, Mar 08 2023 *)
  • PARI
    is(n)=ispseudoprime(n!!! + 3^8) \\ Anders Hellström, Nov 27 2015
  • PARI
    tf(n) = prod(i=0,(n-1)\3, n-3*i);
for(n=1, 1e4, if(ispseudoprime(tf(n) + 3^8), print1(n , ", "))) \\  Altug Alkan, Dec 03 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

Views

Author

Robert Price, Dec 07 2015

Keywords

Comments

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

Examples

			11!3 + 3^9 = 11*8*5*2 + 19683 = 20563 is prime, so 11 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[0, 50000], PrimeQ[MultiFactorial[#, 3] + 3^9] &]
  • PARI
    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

Views

Author

Robert Price, Jan 09 2016

Keywords

Comments

Corresponding primes are 38557, 189757, 17961239276317, 3091650738156317, ... .
a(31) > 50000.

Examples

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

Links

Crossrefs

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

Programs

  • Mathematica
    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

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

A288878 Primes of the form k!3 + 3^2, where k!3 is the triple factorial number (A007661).

Original entry on oeis.org

11, 13, 19, 37, 89, 12329, 209449, 1106569, 24344329, 96342409, 2504902409, 17961239296009, 52580450364682240009, 2295148179742698933452800009, 7825229077844441903818866688000009, 145302140752338100885902776123355299840000009
Offset: 1

Views

Author

Robert Price, Jun 18 2017

Keywords

Links

Crossrefs

Cf. A007661, A247865.

Programs

  • Mathematica
    MultiFactorial[n_, k_] := If[n<1, 1, n*MultiFactorial[n-k, k]];
Select[Table[MultiFactorial[i, 3] + 3^2, {i, 0, 100}], PrimeQ[#]&]

Formula

a(n) = 9 + A007661(A247865(n)). - Elmo R. Oliveira, Apr 13 2025
Previous Showing 11-20 of 118 results. Next

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