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 1-7 of 7 results.

A237443 Numbers m such that (2m)! - m! + 1 is prime.

Original entry on oeis.org

1, 2, 7, 13, 23, 5666, 32918
Offset: 1

Views

Author

Rick L. Shepherd, Feb 07 2014

Keywords

Comments

If it exists, a(7) > 7*10^3. - Michal Paulovic, Feb 17 2024
If it exists, a(8) > 6*10^4. - Kellen Shenton, Dec 21 2024

Examples

			2 is in the sequence because 4! - 2! + 1 = 23 is prime.
7 is in the sequence because 14! - 7! + 1 = 87178286161 is prime.
12 is not in the sequence because 24! - 12! + 1 = 620448401733238960358401 = 587 * 21523 * 49109415278124401.

Crossrefs

Cf. A118812 (corresponding primes).

Programs

  • Mathematica
    Select[Range[100], PrimeQ[(2#)! - #! + 1] &] (* Alonso del Arte, Feb 09 2014 *)
  • PARI
    for(n = 1, 2500, if(isprime((2*n)! - n! + 1), print1(n, ", ")))

Extensions

a(6) from Michal Paulovic, Nov 22 2023
a(7) from Kellen Shenton, Dec 21 2024

A300947 Primes of form (2*k)! + k! + 1.

Original entry on oeis.org

3, 727, 20922789928321, 403291461126605641811020801, 523022617466601111760007224221719391608832001
Offset: 1

Views

Author

Seiichi Manyama, Mar 22 2018

Keywords

Comments

The next term is too large to include.

Crossrefs

Cf. A088332, A118812, A242487.

Programs

  • Maple
    select(isprime,[seq(factorial(2*k)+factorial(k)+1,k=0..600)]); # Muniru A Asiru, May 27 2018
  • PARI
    lista(nn) = {for(k=0, nn, if(ispseudoprime(p=(2*k)!+k!+1), print1(p, ", ")));} \\ Altug Alkan, Mar 22 2018

Formula

a(n) = (2*A242487(n))! + A242487(n)! + 1.

A237579 Least prime factor of (2n)! - n! + 1 (= A237580(n)).

Original entry on oeis.org

2, 23, 5, 59, 7, 59, 87178286161, 29, 11, 443, 13, 587, 403291461126605629356979201, 3307, 17, 43, 19, 131, 83, 2791, 23, 113, 5502622159812088949850305428800254867109635014075023360001, 659, 761, 6108689, 29, 233, 31, 67, 181, 25649409970727, 1561016461, 151, 37, 223, 53, 139, 41, 29209, 43, 61
Offset: 1

Views

Author

M. F. Hasler, Feb 09 2014

Keywords

Comments

For n=0 the expression equals 1 and has no prime factor at all.
The larger terms, and/or those ending in ...01, correspond to indices (listed in A237443) for which the expression itself is a prime (listed in A118812).

Links

Crossrefs

Cf. A237580, A237443, A118812.

Programs

  • PARI
    n -> factor((2*n)!-n!+1)[1,1]

Extensions

a(26)-a(42) from Chai Wah Wu, Oct 15 2019
Typo in a(32) corrected by Seth A. Troisi, May 13 2022

A237580 a(n) = (2n)! - n! + 1.

Original entry on oeis.org

1, 2, 23, 715, 40297, 3628681, 479000881, 87178286161, 20922789847681, 6402373705365121, 2432902008173011201, 1124000727777567763201, 620448401733238960358401, 403291461126605629356979201, 304888344611713860414325708801, 265252859812191058635000805632001
Offset: 0

Views

Author

M. F. Hasler, Feb 09 2014

Keywords

Comments

Primes are listed in A118812, the corresponding indices in A237443; the least prime factor of a(n) in A237579.

Links

Crossrefs

Cf. A000142 (n!), A010050 ((2n)!)

Programs

A118813 Primes of the form (2n)! - n! - 1.

Original entry on oeis.org

3628679, 87178286159, 20922789847679, 265252859812191058635000805631999
Offset: 1

Views

Author

Paolo P. Lava and Giorgio Balzarotti, May 23 2006

Keywords

Comments

The term a(7) (2407 digits) is too large to include even in the b-file.
All the numbers end in 9.
For all n, (2n)! - n! - 1 has exactly A027868(n) trailing 9s. - Rick L. Shepherd, Feb 16 2014
Generated by n = 5, 7, 8, 15, 103, 179, .... - R. J. Mathar, Sep 20 2012 (now A238011)

Examples

			For n=5, (2*5)! - 5! - 1 = 3628800 - 120 - 1 = 3628679, which is prime.

References

  • G. Balzarotti and P. P. Lava, Le sequenze di numeri interi, Hoepli, 2008, p. 159.

Links

Crossrefs

Cf. A238011 (corresponding n), A118812, A237443.

Programs

  • Maple
    PFACT:=proc(N) local i,r; for i from 1 by 1 to N do r:=(2*i)!-i!-1; if isprime(r) then print(i); fi; od; end: PFACT(100);

A233011 Primes of the form (2*n)! - n!^2 - 1.

Original entry on oeis.org

19, 683, 478483199, 20921164185599
Offset: 1

Views

Author

K. D. Bajpai, Dec 03 2013

Keywords

Comments

The 5th term a(5) has 268 digits and is too long to display in data section.
The 7th term a(7) in the sequence has 823 digits.
a(8) has 2030 digits; a(9) has 2264 digits (these are not included in b-file).

Examples

			a(1)= 19: n= 2: (2*n)!- n!^2-1= 19 which is prime.
a(2)= 683: n= 3: (2*n)!- n!^2-1= 683 which is prime.

Links

Crossrefs

Cf. A055490 (primes: n! -1).
Cf. A118812 (primes: (2*n)!-n!+1).

Programs

  • Maple
    KD := proc() local a; a:=(2*n)!-n!^2-1; if isprime(a) then RETURN (a);  fi; end: seq(KD(), n=1..200);

A238011 Numbers k such that (2k)! - k! - 1 is prime.

Original entry on oeis.org

5, 7, 8, 15, 103, 179, 473, 2054, 3595, 4039
Offset: 1

Views

Author

Rick L. Shepherd, Feb 16 2014

Keywords

Comments

No more terms up to 5000. The first six terms are as previously stated in A118813. All terms found and primes proved by OpenPFGW.
No more terms up to 10000. - Michael S. Branicky, Dec 23 2024

Examples

			5 is a term because (2*5)! - 5! - 1 = 3628679 is prime.
4039 is a term because (2*4039)! - 4039! - 1 is prime (28058 digits).

Links

Crossrefs

Cf. A118813 (corresponding primes), A237443, A118812.
Showing 1-7 of 7 results.

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