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.

Showing 1-10 of 43 results. Next

A243078 Numbers k such that k!3 - 3^2 is prime, where k!3 = k!!! is a triple factorial number (A007661).

Original entry on oeis.org

7, 8, 10, 13, 16, 17, 20, 23, 28, 29, 32, 43, 46, 47, 53, 56, 59, 61, 76, 95, 107, 139, 148, 218, 349, 764, 1009, 1130, 1183, 1429, 1516, 2072, 2471, 4937, 10204, 13993, 16249, 18166, 25733, 29033, 40090
Offset: 1

Views

Author

Robert Price, May 30 2014

Keywords

Comments

a(42) > 50000.
k=2 and k=4 produce values (-7 and -5) whose absolute value is a prime.
Terms > 2000 correspond to probable primes.

Examples

			17!3 - 3^2 = 17*14*11*8*5*2 - 9 = 209431 is prime, so 17 is in the sequence. - _Jens Kruse Andersen_, Aug 20 2014

Links

Crossrefs

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

Programs

  • Mathematica
    MultiFactorial[n_,k_]:=If[n<1,1,If[n

Extensions

a(41) from Robert Price, Sep 19 2014

A261145 Numbers n such that n!3 + 3^10 is prime, where n!3 = n!!! is a triple factorial number (A007661).

Original entry on oeis.org

2, 4, 7, 11, 25, 38, 47, 94, 95, 155, 275, 277, 292, 299, 395, 409, 614, 1409, 1963, 3422, 5243, 5884, 5971, 8527, 10882, 13223, 16406, 20851, 28886
Offset: 1

Views

Author

Robert Price, Nov 18 2015

Keywords

Comments

Corresponding primes are: 59051, 59053, 59077, 59929, 608667049, 3091650738235049, 262134882788466747049, ...
a(30) > 50000.
Terms > 47 correspond to probable primes.

Examples

			11!3 + 3^10 = 11*8*5*2 + 59049 = 59929 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, If[n < k + 1, n, n*MultiFactorial[n - k, k]]];
Select[Range[0, 50000], PrimeQ[MultiFactorial[#, 3] + 3^10] &]
  • PARI
    for(n=1, 1e3, if(ispseudoprime(prod(i=0, floor((n-1)/3), n-3*i) + 3^10), print1(n, ", "))) \\ Altug Alkan, Nov 18 2015

A265200 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

8, 10, 11, 13, 16, 19, 20, 22, 37, 38, 47, 73, 92, 94, 100, 218, 241, 284, 482, 541, 736, 787, 829, 916, 1147, 1312, 1856, 1928, 2035, 3134, 4958, 5503, 8042, 16898, 16987, 24548, 25076, 35086
Offset: 1

Views

Author

Robert Price, Dec 04 2015

Keywords

Comments

Corresponding primes are: 2267, 2467, 3067, 5827, 60427, 1108747, 4190987, 24346507, 664565853954187, ...
a(39) > 50000.
Terms > 38 correspond to probable primes.

Examples

			11!3 + 3^7 = 11*8*5*2 + 2187 = 3067 is prime, so 11 is in the sequence.

Links

Crossrefs

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

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] + 3^7] &]
Select[Range[35100],PrimeQ[Times@@Range[#,1,-3]+2187]&] (* Harvey P. Dale, Oct 19 2023 *)
  • PARI
    tf(n) = prod(i=0, (n-1)\3, n-3*i);
for(n=1, 1e4, if(ispseudoprime(tf(n) + 3^7), print1(n , ", "))) \\ Altug Alkan, Dec 04 2015

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

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

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 *)

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] &]
Showing 1-10 of 43 results. Next

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