A006882 -id:A006882 - cp's OEIS frontend

A268645 Union of the factorial numbers (A000142) and the double factorials numbers (A006882).

1, 2, 3, 6, 8, 15, 24, 48, 105, 120, 384, 720, 945, 3840, 5040, 10395, 40320, 46080, 135135, 362880, 645120, 2027025, 3628800, 10321920, 34459425, 39916800, 185794560, 479001600, 654729075, 3715891200, 6227020800, 13749310575, 81749606400, 87178291200, 316234143225, 1307674368000

Offset: 1

Olivier Gérard, Oct 10 2014, revised by N. J. A. Sloane, Feb 09 2016

nonn

Douglas Hoftstadter, Keynote lecture, DIMACS Workshop on Recognition of Integer Sequences, Oct. 10, 2014.

Abstract of D. Hoftstadter in the Workshop's program

Cf. A000142, A006882.

See A248652 for another version.

max = 10^13;
A000142 = Reap[For[k = 0, k!  <= max, k++, Sow[k!]]][[2, 1]];
A006882 = Reap[For[k = 0, k!! <= max, k++, Sow[k!!]]][[2, 1]];
Union[A000142, A006882] (* Jean-François Alcover, Jul 18 2022 *)

A289850 Primes of the form k!2 - 4, where k!2 is the double factorial number (A006882).

Original entry on oeis.org

11, 101, 941, 10391, 135131, 2027021, 654729071, 7905853580621, 221643095476699771871, 79777941814291672401518892224505807820921910393015244140621, 6462013286957625464523030270184970433494674741834234775390621

Offset: 1

Robert Price, Jul 13 2017

nonn

Robert Price, Table of n, a(n) for n = 1..13
Henri and Renaud Lifchitz, PRP Records.Search for n!2-4.
Joe McLean, Interesting Sources of Probable Primes.
OpenPFGW Project, Primality Tester.

Cf. A006882, A123910.

MultiFactorial[n_, k_] := If[n<1, 1, n*MultiFactorial[n-k, k]];
Select[Table[MultiFactorial[i, 2] - 4, {i, 4, 100}], PrimeQ[#]&]
Select[Range[4,100]!!-4,PrimeQ] (* Harvey P. Dale, Dec 16 2020 *)

a(n) = A006882(A123910(n)) - 4. - Elmo R. Oliveira, Apr 14 2025

A289851 Primes of the form k!2 - 8, where k!2 is the double factorial number (A006882).

Original entry on oeis.org

7, 97, 937, 654729067, 13113070457687988603440617, 563862029680583509947946867, 536347102817482913555411512425352545980058003572241486357421867, 352999527454840466971061863960307904899505075341088595453568994140617

Offset: 1

Robert Price, Jul 13 2017

nonn

Robert Price, Table of n, a(n) for n = 1..10
Henri and Renaud Lifchitz, PRP Records.Search for n!2-8.
Joe McLean, Interesting Sources of Probable Primes.
OpenPFGW Project, Primality Tester.

Cf. A006882, A259359.

MultiFactorial[n_, k_] := If[n<1, 1, n*MultiFactorial[n-k, k]];
Select[Table[MultiFactorial[i, 2] - 8, {i, 5, 100}], PrimeQ[#]&]
Select[Range[5,100]!!-8,PrimeQ] (* Harvey P. Dale, Feb 06 2024 *)

a(n) = A006882(A259359(n)) - 8. - Elmo R. Oliveira, Apr 14 2025

Definition corrected by Harvey P. Dale, Feb 06 2024

A289852 Primes of the form k!2 - 16, where k!2 is the double factorial number (A006882).

Original entry on oeis.org

89, 929, 135119, 34459409, 7905853580609, 669325572332691496707919692320662308340434243618803739488329723923351785805848442856791239207612629457179653299076271283992814866750698368061459208762618124485015869140609

Offset: 1

Robert Price, Jul 13 2017

nonn

Robert Price, Table of n, a(n) for n = 1..7
Henri and Renaud Lifchitz, PRP Records.Search for n!2-16.
Joe McLean, Interesting Sources of Probable Primes.
OpenPFGW Project, Primality Tester.

Cf. A006882, A258616.

MultiFactorial[n_, k_] := If[n<1, 1, n*MultiFactorial[n-k, k]];
Select[Table[MultiFactorial[i, 2] - 16, {i, 6, 100}], PrimeQ[#]&]

a(n) = A006882(A258616(n)) - 16. - Elmo R. Oliveira, Apr 14 2025

A289853 Primes of the form k!2 - 32, where k!2 is the double factorial number (A006882).

Original entry on oeis.org

73, 25373791335626257947657609343, 488960130368663401543922783473071784646213671843, 2783097421140216173669833173554685254745646937315554685903182520041762334418182818434647284243799923238034037601108551025390593

Offset: 1

Robert Price, Jul 13 2017

nonn

Robert Price, Table of n, a(n) for n = 1..4
Henri and Renaud Lifchitz, PRP Records.Search for n!2-32.
Joe McLean, Interesting Sources of Probable Primes.
OpenPFGW Project, Primality Tester.

Cf. A006882, A262772.

MultiFactorial[n_, k_] := If[n<1, 1, n*MultiFactorial[n-k, k]];
Select[Table[MultiFactorial[i, 2] - 32, {i, 6, 100}], PrimeQ[#]&]

a(n) = A006882(A262772(n)) - 32. - Elmo R. Oliveira, Apr 14 2025

A289854 Primes of the form k!2 - 64, where k!2 is the double factorial number (A006882).

Original entry on oeis.org

41, 881, 10331, 34459361, 13749310511, 213458046676811, 6190283353629311, 319830986772877770815561, 563862029680583509947946811, 25373791335626257947657609311, 488960130368663401543922783473071784646213671811

Offset: 1

Robert Price, Jul 13 2017

nonn

Robert Price, Table of n, a(n) for n = 1..13
Henri and Renaud Lifchitz, PRP Records.Search for n!2-64.
Joe McLean, Interesting Sources of Probable Primes.
OpenPFGW Project, Primality Tester.

Cf. A006882, A259045.

MultiFactorial[n_, k_] := If[n<1, 1, n*MultiFactorial[n-k, k]];
Select[Table[MultiFactorial[i, 2] - 64, {i, 7, 100}], PrimeQ[#]&]

a(n) = A006882(A259045(n)) - 64. - Elmo R. Oliveira, Apr 14 2025

A289855 Primes of the form k!2 - 128, where k!2 is the double factorial number (A006882).

Original entry on oeis.org

10267, 135007, 13749310447, 1192568192774434123539907640497, 29215606371473169285018060091249259296747, 1009847364737869270905302433221592504062302663202724609247, 34720596058582394465875230149026168047833371128291024141249287753332469144201839599609247

Offset: 1

Robert Price, Jul 13 2017

nonn

Robert Price, Table of n, a(n) for n = 1..10
Henri and Renaud Lifchitz, PRP Records.Search for n!2-128.
Joe McLean, Interesting Sources of Probable Primes.
OpenPFGW Project, Primality Tester.

Cf. A006882, A257864.

MultiFactorial[n_, k_] := If[n<1, 1, n*MultiFactorial[n-k, k]];
Select[Table[MultiFactorial[i, 2] - 128, {i, 8, 100}], PrimeQ[#]&]
Select[Range[8,120]!!-128,PrimeQ] (* Harvey P. Dale, Dec 01 2018 *)

a(n) = A006882(A257864(n)) - 128. - Elmo R. Oliveira, Apr 14 2025

A289856 Primes of the form k!2 - 256, where k!2 is the double factorial number (A006882).

Original entry on oeis.org

10139, 2026769, 13749310319, 213458046676619, 191898783962510369, 157952079428395476360490147277859119, 29215606371473169285018060091249259296619, 2395415678676082004163677716234578672981800778515369

Offset: 1

Robert Price, Jul 13 2017

nonn

Robert Price, Table of n, a(n) for n = 1..12
Henri and Renaud Lifchitz, PRP Records.Search for n!2-256.
Joe McLean, Interesting Sources of Probable Primes.
OpenPFGW Project, Primality Tester.

Cf. A006882, A265114.

MultiFactorial[n_, k_] := If[n<1, 1, n*MultiFactorial[n-k, k]];
Select[Table[MultiFactorial[i, 2] - 256, {i, 8, 100}], PrimeQ[#]&]

a(n) = A006882(A265114(n)) - 256. - Elmo R. Oliveira, Apr 14 2025

A289857 Primes of the form k!2 - 512, where k!2 is the double factorial number (A006882).

Original entry on oeis.org

433, 9883, 13749310063, 316234142713, 25373791335626257947657608863, 7297912393562140321551086320493608726062890113, 79777941814291672401518892224505807820921910393015244140113

Offset: 1

Robert Price, Jul 13 2017

nonn

Robert Price, Table of n, a(n) for n = 1..10
Henri and Renaud Lifchitz, PRP Records.Search for n!2-512.
Joe McLean, Interesting Sources of Probable Primes.
OpenPFGW Project, Primality Tester.

Cf. A006882, A258452.

MultiFactorial[n_, k_] := If[n<1, 1, n*MultiFactorial[n-k, k]];
Select[Table[MultiFactorial[i, 2] - 512, {i, 9, 100}], PrimeQ[#]&]

a(n) = A006882(A258452(n)) - 512. - Elmo R. Oliveira, Apr 14 2025

A289858 Primes of the form k!2 - 1024, where k!2 is the double factorial number (A006882).

Original entry on oeis.org

9371, 34458401, 191898783962509601, 319830986772877770814601, 157952079428395476360490147277858351, 2987435000850314871976096554696085799164511452611632783323554397412108351, 283806325080779912837729172696128150920628587998105114415737667754150389601

Offset: 1

Robert Price, Jul 13 2017

nonn

Robert Price, Table of n, a(n) for n = 1..7
Henri and Renaud Lifchitz, PRP Records.Search for n!2-1024.
Joe McLean, Interesting Sources of Probable Primes.
OpenPFGW Project, Primality Tester.

Cf. A006882, A258866.

MultiFactorial[n_, k_] := If[n<1, 1, n*MultiFactorial[n-k, k]];
Select[Table[MultiFactorial[i, 2] - 1024, {i, 10, 100}], PrimeQ[#]&]

a(n) = A006882(A258866(n)) - 1024. - Elmo R. Oliveira, Apr 15 2025

cp's OEIS Frontend

A268645 Union of the factorial numbers (A000142) and the double factorials numbers (A006882).

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A289850 Primes of the form k!2 - 4, where k!2 is the double factorial number (A006882).

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Mathematica

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A289851 Primes of the form k!2 - 8, where k!2 is the double factorial number (A006882).

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Extensions

A289852 Primes of the form k!2 - 16, where k!2 is the double factorial number (A006882).

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Mathematica

Formula

A289853 Primes of the form k!2 - 32, where k!2 is the double factorial number (A006882).

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Author

Keywords

Links

Crossrefs

Programs

Mathematica

Formula

A289854 Primes of the form k!2 - 64, where k!2 is the double factorial number (A006882).

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

Formula

A289855 Primes of the form k!2 - 128, where k!2 is the double factorial number (A006882).

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

Formula

A289856 Primes of the form k!2 - 256, where k!2 is the double factorial number (A006882).

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

Formula

A289857 Primes of the form k!2 - 512, where k!2 is the double factorial number (A006882).

Views

Author

Keywords

Links

Crossrefs