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 51 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

A258616 Numbers n such that n!!-16 is prime.

Original entry on oeis.org

7, 9, 13, 17, 25, 185, 197, 261, 407, 593, 1535, 2129, 2139, 2581, 4133, 4665, 15787, 25337, 27449
Offset: 1

Views

Author

Robert Price, Jun 05 2015

Keywords

Comments

Corresponding primes are 89, 929, 135119, 34459409, ... .
a(20) > 50000.

Links

Crossrefs

Cf. A006882, A007749, A094144, A123910.

Programs

  • Mathematica
    Select[Range[4,1000],PrimeQ[#!!-16]&] (* Robert Price, Jun 05 2015 *)
Do[f=n!! - 16; If[PrimeQ[f], Print[{n, f}]], {n, 4, 600}] (* Vincenzo Librandi, Jun 06 2015 *) (see comment)

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

A262772 Numbers k such that k!! - 32 is prime.

Original entry on oeis.org

7, 45, 67, 145, 411, 825, 1021, 4039, 9069, 9789, 12463, 15137, 26313, 27499
Offset: 1

Views

Author

Robert Price, Sep 30 2015

Keywords

Comments

Corresponding primes are 73, 25373791335626257947657609343, ... .
a(15) > 50000.

Links

Crossrefs

Cf. A006882, A007749, A094144, A123910, A258616.

Programs

  • Magma
    DoubleFactorial:=func< n | &*[n..2 by -2] >; [ n: n in [7..450] | IsPrime(DoubleFactorial(n) -32) ]; // Vincenzo Librandi, Oct 01 2015
  • Mathematica
    Select[Range[0, 50000], If[#!! - 32 > 0, PrimeQ[#!! - 32]] &]
  • PARI
    for(n=1, 1e4, if (isprime(prod(k=0, (n-1)\2, n - 2*k ) - 32),print1(n", "))) \\ Altug Alkan, Oct 01 2015

A258452 Numbers n such that n!! - 512 is prime.

Original entry on oeis.org

9, 11, 21, 23, 45, 65, 79, 153, 155, 199, 361, 799, 883, 1237, 1253, 1753, 4975, 5117, 5843, 8179, 12831
Offset: 1

Views

Author

Robert Price, Nov 05 2015

Keywords

Comments

Corresponding primes are 433, 9883, 13749310063, 316234142713, ... .
a(22) > 50000.

Links

Crossrefs

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

Programs

  • Mathematica
    Select[Range[0, 50000], If[#!! - 512 > 0, PrimeQ[#!! - 512]] &]
  • PARI
    for(n=1, 1e4, if (ispseudoprime(m=prod(k=0, (n-1)\2, n - 2*k) - 512), print1(n", "))) \\ Altug Alkan, Nov 06 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

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

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

A258866 Numbers k such that k!! - 1024 is prime.

Original entry on oeis.org

11, 17, 31, 39, 53, 93, 95, 381, 727, 867, 1229, 1573, 3161, 4293, 5635, 7077, 7093, 8861, 37401
Offset: 1

Views

Author

Robert Price, Nov 06 2015

Keywords

Comments

Corresponding primes are 9371, 34458401, ... .
a(20) > 50000.

Links

Crossrefs

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

Programs

  • Mathematica
    Select[Range[0, 50000], If[#!! - 1024 > 0, PrimeQ[#!! - 1024]] &]

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 *)
Showing 1-10 of 51 results. Next

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

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