A007662 -id:A007662 - cp's OEIS frontend

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

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

Robert Price, Mar 10 2017

nonn

a(51) > 10^5.

The first 10 primes associated with this sequence: 3, 3, 5, 7, 23, 47, 233, 587, 3467, 65837.

C. Caldwell and H. Dubner (Eds): The top ten prime numbers: from the unpublished collections of R. Ondrejka (May 2001), Table 21 F, p. 75
Ken Davis, Status of Search for Multifactorial Primes.

Cf. A076185, A085158, A094144, A204657.

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 *)

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

A114779 Cumulative product of quadruple factorial A007662.

Original entry on oeis.org

1, 1, 2, 6, 24, 120, 1440, 30240, 967680, 43545600, 5225472000, 1207084032000, 463520268288000, 271159356948480000, 455547719673446400000, 1578472848668491776000000, 9698137182219213471744000000

Offset: 0

Jonathan Vos Post, Feb 18 2006

			a(10) = 1!!!! * 2!!!! * 3!!!! * 4!!!! * 5!!!! * 6!!!! * 7!!!! * 8!!!! * 9!!!! * 10!!!! = 1 * 2 * 3 * 4 * 5 * 12 * 21 * 32 * 45 * 120 = 5225472000 = 2^13 * 3^6 * 5^3 * 7.

Eric Weisstein's World of Mathematics, Multifactorial.

Cf. A006882, A007662, A000178, A114347.

a(n) = Product_{j=0..n} j!!!!.
a(n) = Product_{j=0..n} A007662(j).
a(n) = n!!!! * a(n-1) where a(0) = 1, a(1) = 1 and n >= 2.
a(n) = n*(n-4)!!!! * a(n-1) where a(0) = 1, a(1) = 1, a(2) = 2.

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

Robert Price, Mar 10 2017

nonn

a(45) > 10^5.

The first 9 primes associated with this sequence: 2, 3, 19, 43, 229, 3463, 208843, 5221123, 151412623.

C. Caldwell and H. Dubner (Eds): The top ten prime numbers: from the unpublished collections of R. Ondrejka (May 2001), Table 21 F, p. 75
Ken Davis, Status of Search for Multifactorial Primes.

Cf. A076185, A085158, A094144, A204657.

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

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

A288890 Primes of the form k!4+2, where k!4 is the quadruple factorial number (A007662).

Original entry on oeis.org

3, 5, 7, 23, 47, 233, 587, 3467, 65837, 40883537, 151412627, 1267389587, 74389431691577, 885821206052908127, 13005556505149168230729834377, 583723376551025432768079734666930727861956890308512536691015627

Offset: 1

Robert Price, Jun 18 2017

nonn

Robert Price, Table of n, a(n) for n = 1..22
Henri& Renaud Lifchitz, PRP Records.Search for n!4+2.
Joe McLean, Interesting Sources of Probable Primes
OpenPFGW Project, Primality Tester

Cf. A007662, A283553.

MultiFactorial[n_, k_] := If[n<1, 1, n*MultiFactorial[n-k, k]];
Select[Table[MultiFactorial[i, 4] + 2, {i, 0, 100}], PrimeQ[#]&]
Select[Table[Times@@Range[k,1,-4]+2,{k,150}],PrimeQ] (* Harvey P. Dale, Nov 24 2024 *)

A289490 Primes of the form k!4+8, where k!4 is the quadruple factorial number (A007662).

Original entry on oeis.org

11, 13, 29, 53, 239, 593, 65843, 1514213, 5221133, 4996616633, 1729986783533, 7579867420133, 36453104912477522894633, 2442358029135994033939883, 173407420068655576409731133, 534602198949923693866675351078133, 7419136758370889359733910587728133

Offset: 1

Robert Price, Sep 02 2017

nonn

Robert Price, Table of n, a(n) for n = 1..22
Henri& Renaud Lifchitz, PRP Records.Search for n!4+8.
Joe McLean, Interesting Sources of Probable Primes
OpenPFGW Project, Primality Tester

Cf. A291343.

MultiFactorial[n_, k_] := If[n<1, 1, n*MultiFactorial[n-k, k]];
Select[Table[MultiFactorial[i, 4] + 8, {i, 0, 100}], PrimeQ[#]&]

A289492 Primes of the form k!4+16, where k!4 is the quadruple factorial number (A007662).

Original entry on oeis.org

17, 19, 37, 61, 601, 65851, 40883551, 44358635491, 184874815141, 200200021673987500790641, 2442358029135994033939891, 13005556505149168230729834391, 85277434004263096088895523996891, 47579595706543208754134106245953141

Offset: 1

Robert Price, Sep 02 2017

nonn

Robert Price, Table of n, a(n) for n = 1..18
Henri& Renaud Lifchitz, PRP Records.Search for n!4+16.
Joe McLean, Interesting Sources of Probable Primes
OpenPFGW Project, Primality Tester

Cf. A291344.

MultiFactorial[n_, k_] := If[n<1, 1, n*MultiFactorial[n-k, k]];
Select[Table[MultiFactorial[i, 4] + 16, {i, 0, 100}], PrimeQ[#]&]

A289510 Primes of the form k!4+32, where k!4 is the quadruple factorial number (A007662).

Original entry on oeis.org

37, 53, 263, 617, 65867, 208877, 5221157, 40883567, 44358635507, 184874815157, 178311467764705307, 9807130727058790157, 200200021673987500790657, 173407420068655576409731157, 4551830726072842264843919206776501006328157

Offset: 1

Robert Price, Sep 02 2017

nonn

Robert Price, Table of n, a(n) for n = 1..23
Henri& Renaud Lifchitz, PRP Records.Search for n!4+32.
Joe McLean, Interesting Sources of Probable Primes
OpenPFGW Project, Primality Tester

Cf. A291345.

MultiFactorial[n_, k_] := If[n<1, 1, n*MultiFactorial[n-k, k]];
Select[Table[MultiFactorial[i, 4] + 32, {i, 0, 100}], PrimeQ[#]&]

A289518 Primes of the form k!4+64, where k!4 is the quadruple factorial number (A007662).

Original entry on oeis.org

67, 109, 3529, 10009, 65899, 151412689, 1267389649, 341094033905689, 9807130727058790189, 36453104912477522894689, 1008407509171875041482378189, 43350768819741354903275421016919057203189, 29366774490668885282893783501883117566129541193767295703189

Offset: 1

Robert Price, Sep 02 2017

nonn

Robert Price, Table of n, a(n) for n = 1..16
Henri& Renaud Lifchitz, PRP Records.Search for n!4+64.
Joe McLean, Interesting Sources of Probable Primes
OpenPFGW Project, Primality Tester

Cf. A291347.

MultiFactorial[n_, k_] := If[n<1, 1, n*MultiFactorial[n-k, k]];
Select[Table[MultiFactorial[i, 4] + 64, {i, 0, 100}], PrimeQ[#]&]
Select[Table[Times@@Range[n,1,-4]+64,{n,200}],PrimeQ] (* Harvey P. Dale, May 31 2020 *)

A289519 Primes of the form k!4+128, where k!4 is the quadruple factorial number (A007662).

Original entry on oeis.org

131, 149, 173, 359, 3593, 65963, 151412753, 184874815253, 675141445011750931735785863483259503, 13075173582607657311300240428800205506303238072109503, 12956907789303111531153065870401861366351857094178052776930473828253

Offset: 1

Robert Price, Sep 02 2017

nonn

Robert Price, Table of n, a(n) for n = 1..12
Henri& Renaud Lifchitz, PRP Records.Search for n!4+128.
Joe McLean, Interesting Sources of Probable Primes
OpenPFGW Project, Primality Tester

Cf. A291348.

MultiFactorial[n_, k_] := If[n<1, 1, n*MultiFactorial[n-k, k]];
Select[Table[MultiFactorial[i, 4] + 128, {i, 0, 100}], PrimeQ[#]&]
Select[Table[Times@@Range[n,1,-4]+128,{n,200}],PrimeQ] (* Harvey P. Dale, Aug 13 2023 *)

A289560 Primes of the form k!4+256, where k!4 is the quadruple factorial number (A007662).

Original entry on oeis.org

257, 277, 487, 1267389841, 50491808745015763381, 1008407509171875041482378381, 429215532868726286171043772444743140881, 4551830726072842264843919206776501006328381

Offset: 1

Robert Price, Sep 02 2017

nonn

Harvey P. Dale, Table of n, a(n) for n = 1..17
Henri& Renaud Lifchitz, PRP Records.Search for n!4+256.
Joe McLean, Interesting Sources of Probable Primes
OpenPFGW Project, Primality Tester

Cf. A291349.

MultiFactorial[n_, k_] := If[n<1, 1, n*MultiFactorial[n-k, k]];
Select[Table[MultiFactorial[i, 4] + 256, {i, 0, 100}], PrimeQ[#]&]
Select[Table[256+Times@@Range[n,1,-4],{n,200}],PrimeQ] (* Harvey P. Dale, Nov 04 2024 *)

cp's OEIS Frontend

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

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A114779 Cumulative product of quadruple factorial A007662.

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

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A288890 Primes of the form k!4+2, where k!4 is the quadruple factorial number (A007662).

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A289490 Primes of the form k!4+8, where k!4 is the quadruple factorial number (A007662).

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A289492 Primes of the form k!4+16, where k!4 is the quadruple factorial number (A007662).

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A289510 Primes of the form k!4+32, where k!4 is the quadruple factorial number (A007662).

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A289518 Primes of the form k!4+64, where k!4 is the quadruple factorial number (A007662).

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A289519 Primes of the form k!4+128, where k!4 is the quadruple factorial number (A007662).

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Programs

Mathematica

A289560 Primes of the form k!4+256, where k!4 is the quadruple factorial number (A007662).

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