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 1-5 of 5 results.

A049433 Numbers k such that k! - (k-1)! - 1 is prime.

Original entry on oeis.org

3, 4, 6, 8, 9, 12, 28, 78, 99, 184, 286, 291, 398, 411, 600, 718, 732, 889, 1963, 2240, 2242, 2533, 8800, 11403, 18335, 20277, 21029
Offset: 1

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Author

Paul Jobling (paul.jobling(AT)whitecross.com)

Keywords

Comments

There is no further term up to 1400. - Farideh Firoozbakht, Jul 18 2003
a(25) > 12000. [Donovan Johnson, Dec 18 2009]

Examples

			6 is a term since 6! - (6-1)! - 1 = 599 is prime.
		

Crossrefs

Formula

a(n) = A090704(n) + 1 = n*n! + 1 = ((n+1)-1)*n! + 1 = (n+1)! - n! + 1 .

Extensions

More terms from Farideh Firoozbakht, Jul 18 2003
Corrected offset, edited definition and a(19)-a(24) from Donovan Johnson, Dec 18 2009
a(25)-a(27) from Michael S. Branicky, Jun 13 2025

A049984 Primes of the form n! - (n-1)! + 1.

Original entry on oeis.org

2, 5, 19, 97, 601, 35281, 5748019201, 2311256907767808001, 594596384994354462720001, 5382999938946608755288342267304597177897268019200000000001, 136332557214406957166109544809874331662074014454506289616400595025920000000000001
Offset: 1

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Author

Keywords

Comments

Primes in A188914.

Crossrefs

Cf. A188914. For more terms, see A049432.

Programs

Formula

a(n) = A188914(A049432(n)). - Elmo R. Oliveira, Feb 18 2025

A090703 Numbers k such that k*k! + 1 is prime.

Original entry on oeis.org

1, 2, 3, 4, 5, 7, 12, 19, 23, 45, 58, 149, 151, 197, 682, 879, 1134, 1906, 6616, 10242, 12015
Offset: 1

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Author

mohammed bouayoun (bouyao(AT)wanadoo.fr), Jan 15 2004

Keywords

Examples

			3*3! + 1 = 19 and 19 is prime, so 3 is a member.
		

Crossrefs

Cf. A049432.

Programs

  • Mathematica
    Do[If[PrimeQ[n*n! + 1], Print[n]], {n, 0, 2000}] (* Mohammed Bouayoun (mohammed.bouayoun(AT)sanef.com), May 05 2006 *)
  • PARI
    isok(k) = ispseudoprime(k*k! + 1); \\ Altug Alkan, Mar 22 2018

Formula

a(n) = A049432(n) - 1.

Extensions

a(17) from Mohammed Bouayoun (mohammed.bouayoun(AT)sanef.com), May 05 2006
a(18)-a(19) from Jason Earls, Jan 24 2008
a(20) from Seiichi Manyama (by using the data calculated by Donovan Johnson, Dec 18 2009), Mar 22 2018
a(21) from Michael S. Branicky, Jun 11 2025

A245495 Primes of the form n! - (n+1)! + (n+2)! + 1.

Original entry on oeis.org

103, 4441, 36650881, 5787936001, 19702293811201, 1075342687614074880001, 8547762518578406446202880000001, 59043709472234119545920159524322926688993280000000001, 698533028148544417308552639358841460358000936394290829866303488000000000001
Offset: 1

Views

Author

K. D. Bajpai, Jul 24 2014

Keywords

Comments

The next term a(10) has 95 digits which is too large to show in data section.
a(16) has 1181 digits, hence not included in b-file.
Primes for indices 3, 5, 9, 11, 14, 20, 27, 41, 54, 65, 81, 83, 105, 315, 323, 515, ... - Robert G. Wilson v, Aug 07 2014

Examples

			m = 3: m! - (m+1)! + (m+2)! + 1 = 103, which is prime, hence appears in the sequence.
m = 5: m! - (m+1)! + (m+2)! + 1 = 4441, which is prime, hence appears in the sequence.
		

Crossrefs

Programs

  • Mathematica
    Select[Table[n! - (n + 1)! + (n + 2)! + 1, {n, 200}], PrimeQ[#] &]
    Select[#[[1]]-#[[2]]+#[[3]]+1&/@Partition[Range[70]!,3,1],PrimeQ] (* Harvey P. Dale, Aug 20 2021 *)
  • PARI
    a(n) = p=n!-(n+1)!+(n+2)!+1;if(ispseudoprime(p),return(p))
    n=1;while(n<100,if(a(n),print1(a(n),", "));n++) \\ Derek Orr, Jul 27 2014

A245528 Primes of the form n! - (n + 1)! + (n + 2)! - 1.

Original entry on oeis.org

19, 101, 35999, 327599, 3306239, 81430271999, 24779106953279078399999, 10501089199335077511167999999, 1372369506422963989169318155460666934165503999999999, 117024364553755119629556890816711613171571359743999999999
Offset: 1

Views

Author

K. D. Bajpai, Jul 25 2014

Keywords

Comments

The term a(11) has 129 digits which is too large to show in data section.
a(15) has 1081 digits, hence not included in b-file.
The first 20 primes are for n = 2, 3, 6, 7, 8, 12, 21, 25, 40, 43, 83, 107, 132, 139, 478, 505, 931, 1516, 1739, 5208. - Jens Kruse Andersen, Aug 10 2014

Examples

			m = 2: m! - (m + 1)! + (m + 2)! - 1 = 19 which is prime, hence appears in the sequence.
m = 6: m! - (m + 1)! + (m + 2)! - 1 = 35999 which is prime, hence appears in the sequence.
		

Crossrefs

Programs

  • Magma
    [a: n in [0..100] | IsPrime(a) where a is Factorial(n) - Factorial(n + 1) + Factorial(n + 2) - 1 ]; // Vincenzo Librandi, Aug 11 2014
  • Mathematica
    Select[Table[n! - (n + 1)! + (n + 2)! - 1, {n, 200}], PrimeQ[#] &]
  • PARI
    for(n=1,200,s=n!-(n+1)!+(n+2)!-1;if(ispseudoprime(s),print1(s,", "))) \\ Derek Orr, Aug 10 2014
    
Showing 1-5 of 5 results.