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 1-6 of 6 results.

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

A265201 Numbers n such that n!!! - 3^10 is prime, where n!3 = n!!! is a triple factorial number (A007661).

Original entry on oeis.org

19, 20, 22, 26, 41, 55, 56, 152, 155, 316, 347, 383, 500, 556, 646, 656, 748, 976, 1433, 2213, 2680, 2911, 3373, 4799, 4964, 7189, 8798, 9871, 14069, 14627, 16657, 20230, 24137, 24430, 28331, 36313, 41522, 43031, 46072, 47719
Offset: 1

Views

Author

Robert Price, Dec 04 2015

Keywords

Comments

Corresponding primes are 1047511, 4129751, 24285271, 2504843351, 126757680265156951, ... .
a(41) > 50000.

Examples

			19!3 - 3^10 = 19*16*13*10*7*4*1 - 59049 = 1047511 is prime, so 19 is in the sequence.

Links

Crossrefs

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

Programs

  • Mathematica
    MultiFactorial[n_, k_] := If[n < 1, 1, If[n < k + 1, n, n*MultiFactorial[n - k, k]]];
Select[Range[17, 50000], PrimeQ[MultiFactorial[#, 3] - 3^10] &]
  • PARI
    tf(n) = prod(i=0, (n-1)\3, n-3*i);
for(n=1, 1e4, if(ispseudoprime(tf(n) - 3^10), print1(n , ", "))) \\ Altug Alkan, Dec 04 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 *)

A288886 Primes of the form k!3 + 3^10, where k!3 is the triple factorial number (A007661).

Original entry on oeis.org

59051, 59053, 59077, 59929, 608667049, 3091650738235049, 262134882788466747049, 17994728558292550488813850298696914425610240059049, 113024723205613715155108333435313153533542400059049
Offset: 1

Views

Author

Robert Price, Jun 18 2017

Keywords

Links

Crossrefs

Cf. A007661, A261145.

Programs

  • Mathematica
    MultiFactorial[n_, k_] := If[n<1, 1, n*MultiFactorial[n-k, k]];
Select[Table[MultiFactorial[i, 3] + 3^10, {i, 0, 100}], PrimeQ[#]&]
Select[Table[Times@@Range[n,1,-3]+59049,{n,150}],PrimeQ] (* Harvey P. Dale, May 03 2020 *)

Formula

a(n) = 59049 + A007661(A261145(n)). - Elmo R. Oliveira, Apr 14 2025
Showing 1-6 of 6 results.

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