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.

Previous Showing 11-18 of 18 results.

A283553 Numbers k such that k![4] + 2 is prime, where k![4] = A007662(k) = quadruple factorial.

Original entry on oeis.org

0, 1, 3, 5, 7, 9, 11, 13, 15, 19, 27, 29, 31, 43, 53, 75, 143, 169, 185, 235, 259, 363, 365, 457, 493, 573, 777, 1273, 1275, 1865, 3621, 4523, 5291, 5845, 7185, 10183, 12845, 15057, 16281, 17945, 18771, 22479, 27235, 28089, 31557, 39163, 45709, 46329, 52211, 77779
Offset: 1

Views

Author

Robert Price, Mar 10 2017

Keywords

Comments

a(51) > 10^5.
The first 10 primes associated with this sequence: 3, 3, 5, 7, 23, 47, 233, 587, 3467, 65837.

Links

Crossrefs

Cf. A076185, A085158, A094144, A204657.

Programs

  • Mathematica
    MultiFactorial[n_, k_] := If[n < 1, 1, n*MultiFactorial[n - k, k]];
Select[Range[0, 50000], PrimeQ[MultiFactorial[#, 4] + 2] &]
Select[Range[0,78000],PrimeQ[Times@@Range[#,1,-4]+2]&] (* Harvey P. Dale, Aug 16 2023 *)

Extensions

a(49)-a(50) from Robert Price, Aug 12 2017

A257864 Numbers n such that n!! - 2^7 is prime.

Original entry on oeis.org

11, 13, 21, 47, 59, 77, 109, 129, 155, 163, 245, 337, 511, 1417, 3013, 3757, 4989, 8977, 12479, 12869
Offset: 1

Views

Author

Robert Price, May 11 2015

Keywords

Comments

a(21) > 50000. - Robert Price, May 11 2015
a(n) is odd. - Chai Wah Wu, May 12 2015

Links

Crossrefs

Cf. A007749, A094144, A123910 (other forms of n!!-2^k)
Cf. A080778, A076185, A076186, A076188, A076189, A076190, A076193, A076194, A076195, A076196, A076197 (other forms of n!!+2^k)

Programs

  • Mathematica
    Select[Range[0, 50000], #!! - 128 > 0 && PrimeQ[#!! - 128] &]
  • PARI
    is(n)=ispseudoprime(prod(i=0,(n-1)\2, n-2*i)-128) \\ Charles R Greathouse IV, May 11 2015
  • Perl
    use ntheory ":all"; use Math::GMPz;
sub mf2 { my($n,$P)=(shift,Math::GMPz->new(1)); $P *= $n-($_<<1) for 0..($n-1)>>1; $P; }
for (1..100000) { say if is_prob_prime(mf2($)-128) } # _Dana Jacobsen, May 13 2015
  • Python
    from gmpy2 import is_prime, mpz
A257864_list, g, h = [], mpz(105), mpz(128)
for i in range(9,10**5,2):
    g *= i
    if is_prime(g-h):
        A257864_list.append(i) # Chai Wah Wu, May 12 2015

A259045 Numbers n such that n!! - 2^6 is prime.

Original entry on oeis.org

7, 9, 11, 17, 21, 27, 29, 39, 43, 45, 67, 145, 173, 613, 833, 1449, 1703, 1719, 2673, 19661, 36095, 37837, 37845
Offset: 1

Views

Author

Robert Price, Jun 17 2015

Keywords

Comments

a(24) > 50000.

Links

Crossrefs

Cf. A007749, A094144, A123910, A257864 (other forms of n!!-2^k)
Cf. A080778, A076185, A076186, A076188, A076189, A076190, A076193, A076194, A076195, A076196, A076197 (other forms of n!!+2^k)

Programs

  • Mathematica
    Select[Range[0, 50000], #!! - 64 > 0 && PrimeQ[#!! - 64] &]
Select[Range[4, 6000], PrimeQ[#!! - 64] &] (* Vincenzo Librandi, Jun 18 2015 *)

A283485 Numbers k such that k![6]-2 is prime, where k![6] = A085158 (k) = sextuple factorial.

Original entry on oeis.org

4, 5, 7, 11, 13, 23, 25, 31, 33, 37, 59, 63, 91, 157, 265, 267, 327, 539, 555, 621, 715, 921, 979, 1633, 1821, 2259, 2697, 2809, 2863, 2935, 4213, 4351, 5937, 6885, 8743, 10761, 15159, 17685, 52075, 55147, 68677, 99655
Offset: 1

Views

Author

Robert Price, Mar 08 2017

Keywords

Comments

a(43) > 10^5.
The first 10 primes associated with this sequence: 2, 3, 5, 53, 89, 21503, 43223, 1339973, 7577953, 49579073.

Links

Crossrefs

Cf. A076185, A085158, A094144, A204657.

Programs

  • Mathematica
    MultiFactorial[n_, k_] := If[n < 1, 1, n*MultiFactorial[n - k, k]];
Select[Range[2, 50000], PrimeQ[MultiFactorial[#, 6] - 2] &]
Select[Range[100000],PrimeQ[Times@@Range[#,1,-6]-2]&] (* Harvey P. Dale, Feb 23 2023 *)

Extensions

a(39)-a(42) from Robert Price, Jul 09 2017

A283554 Numbers k such that k![4] - 2 is prime, where k![4] = A007662(k) = quadruple factorial.

Original entry on oeis.org

4, 5, 7, 9, 11, 15, 21, 25, 29, 49, 79, 87, 95, 125, 133, 153, 157, 185, 201, 217, 223, 289, 323, 469, 533, 567, 821, 1001, 1999, 2523, 2533, 2827, 2843, 4821, 8153, 8947, 12739, 19353, 22929, 30629, 31809, 37785, 74913, 97411
Offset: 1

Views

Author

Robert Price, Mar 10 2017

Keywords

Comments

a(45) > 10^5.
The first 9 primes associated with this sequence: 2, 3, 19, 43, 229, 3463, 208843, 5221123, 151412623.

Links

Crossrefs

Cf. A076185, A085158, A094144, A204657.

Programs

  • Mathematica
    MultiFactorial[n_, k_] := If[n < 1, 1, n*MultiFactorial[n - k, k]];
Select[Range[2, 50000], PrimeQ[MultiFactorial[#, 4] - 2] &]

Extensions

a(43)-a(44) from Robert Price, Jul 24 2017

A283559 Numbers k such that k![10]-2 is prime, where k![10] is the ten-fold multifactorial.

Original entry on oeis.org

4, 5, 7, 9, 13, 15, 21, 25, 29, 31, 33, 41, 45, 49, 77, 195, 197, 199, 211, 309, 319, 345, 349, 395, 509, 533, 539, 597, 615, 705, 781, 803, 869, 969, 1313, 1317, 1331, 1335, 1337, 1429, 1597, 2121, 2133, 2513, 2547, 2733, 2885, 2931, 3701, 3709, 4681, 5911, 5933, 6125, 8191, 10637, 10679, 10845, 14901, 15629, 17165, 21691, 21867, 23119, 27033, 28601, 31245, 31957, 33289, 35773, 45011, 51079, 63241, 81369, 92615
Offset: 1

Views

Author

Robert Price, Mar 10 2017

Keywords

Comments

a(76) > 50000.
The first 13 primes associated with this sequence: 2, 3, 5, 7, 37, 73, 229, 1873, 4957, 7159, 29599, 293599, 2953123.

Links

Crossrefs

Cf. A076185, A085158, A094144, A204657.

Programs

  • Mathematica
    MultiFactorial[n_, k_] := If[n < 1, 1, n*MultiFactorial[n - k, k]];
Select[Range[2, 50000], PrimeQ[MultiFactorial[#, 10] - 2] &]

Extensions

a(72)-a(75) from Robert Price, Apr 03 2017

A283594 Numbers k such that k![12]+2 is prime, where k![12] is the twelve-fold multifactorial.

Original entry on oeis.org

0, 1, 3, 5, 9, 11, 15, 21, 27, 29, 39, 99, 159, 213, 249, 351, 443, 489, 513, 563, 705, 1059, 1599, 1733, 2361, 3699, 4263, 4451, 4479, 5141, 5751, 7355, 7461, 8525, 8861, 18231, 19629, 23571, 41789, 76973, 86997, 93735, 98943
Offset: 1

Views

Author

Robert Price, Mar 11 2017

Keywords

Comments

a(44) > 10^5.
The first 12 primes associated with this sequence: 3, 3, 5, 7, 11, 13, 47, 191, 1217, 2467, 47387.

Links

Crossrefs

Cf. A076185, A085158, A094144, A204657.

Programs

  • Mathematica
    MultiFactorial[n_, k_] := If[n < 1, 1, n*MultiFactorial[n - k, k]];
Select[Range[0, 50000], PrimeQ[MultiFactorial[#, 12] + 2] &]

Extensions

a(40)-a(43) from Robert Price, Mar 24 2017

A287207 Numbers k such that k![6] + 2 is prime, where k![6] = A085158(k) = sextuple factorial.

Original entry on oeis.org

0, 1, 3, 5, 9, 17, 27, 45, 51, 53, 93, 197, 213, 221, 245, 279, 845, 927, 2055, 2895, 3615, 5613, 12753, 15737, 17813, 18545, 22629, 47859, 48797
Offset: 1

Views

Author

Robert Price, May 21 2017

Keywords

Comments

a(30) > 50000.
The first 7 primes associated with this sequence: 3, 3, 5, 7, 29, 937, 229637.

Links

Crossrefs

Cf. A076185, A085158, A094144, A204657.

Programs

  • Mathematica
    MultiFactorial[n_, k_] := If[n < 1, 1, n*MultiFactorial[n - k, k]];
Select[Range[0, 50000], PrimeQ[MultiFactorial[#, 6] + 2] &]
Select[Range[0,10000],PrimeQ[Times@@Range[#,1,-6]+2]&] (* The program generates the first 22 terms of the sequence. *) (* Harvey P. Dale, Dec 27 2022 *)
Previous Showing 11-18 of 18 results.

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

Content is available under The OEIS End-User License Agreement.