A204657 -id:A204657 - cp's OEIS frontend

A283559 Numbers k such that k![10]-2 is prime, where k![10] is the ten-fold multifactorial.

4, 5, 7, 9, 13, 15, 21, 25, 29, 31, 33, 41, 45, 49, 77, 195, 197, 199, 211, 309, 319, 345, 349, 395, 509, 533, 539, 597, 615, 705, 781, 803, 869, 969, 1313, 1317, 1331, 1335, 1337, 1429, 1597, 2121, 2133, 2513, 2547, 2733, 2885, 2931, 3701, 3709, 4681, 5911, 5933, 6125, 8191, 10637, 10679, 10845, 14901, 15629, 17165, 21691, 21867, 23119, 27033, 28601, 31245, 31957, 33289, 35773, 45011, 51079, 63241, 81369, 92615

Offset: 1

Robert Price, Mar 10 2017

nonn

a(76) > 50000.

The first 13 primes associated with this sequence: 2, 3, 5, 7, 37, 73, 229, 1873, 4957, 7159, 29599, 293599, 2953123.

C. Caldwell and H. Dubner (Eds): The top ten prime numbers: from the unpublished collections of R. Ondrejka (May 2001), Table 21 F, p. 75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[#, 10] - 2] &]

a(72)-a(75) from Robert Price, Apr 03 2017

A283594 Numbers k such that k![12]+2 is prime, where k![12] is the twelve-fold multifactorial.

Original entry on oeis.org

0, 1, 3, 5, 9, 11, 15, 21, 27, 29, 39, 99, 159, 213, 249, 351, 443, 489, 513, 563, 705, 1059, 1599, 1733, 2361, 3699, 4263, 4451, 4479, 5141, 5751, 7355, 7461, 8525, 8861, 18231, 19629, 23571, 41789, 76973, 86997, 93735, 98943

Offset: 1

Robert Price, Mar 11 2017

nonn

a(44) > 10^5.

The first 12 primes associated with this sequence: 3, 3, 5, 7, 11, 13, 47, 191, 1217, 2467, 47387.

C. Caldwell and H. Dubner (Eds): The top ten prime numbers: from the unpublished collections of R. Ondrejka (May 2001), Table 21 F, p. 75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[#, 12] + 2] &]

a(40)-a(43) from Robert Price, Mar 24 2017

A287207 Numbers k such that k![6] + 2 is prime, where k![6] = A085158(k) = sextuple factorial.

Original entry on oeis.org

0, 1, 3, 5, 9, 17, 27, 45, 51, 53, 93, 197, 213, 221, 245, 279, 845, 927, 2055, 2895, 3615, 5613, 12753, 15737, 17813, 18545, 22629, 47859, 48797

Offset: 1

Robert Price, May 21 2017

nonn

a(30) > 50000.

The first 7 primes associated with this sequence: 3, 3, 5, 7, 29, 937, 229637.

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[#, 6] + 2] &]
Select[Range[0,10000],PrimeQ[Times@@Range[#,1,-6]+2]&] (* The program generates the first 22 terms of the sequence. *) (* Harvey P. Dale, Dec 27 2022 *)

A288370 Primes of the form k!10 + 2, where k!10 is the decuple factorial number (A288327).

Original entry on oeis.org

3, 5, 7, 11, 13, 41, 173, 233, 1877, 293603, 318482201, 3047775608243, 22045250515087152640289, 1302844523174285888671877, 930620100318118916029523201, 4831436058626442432403564453127, 2060356301148292483532951454058361, 9936127455089061347552058319626135203

Offset: 1

Robert Price, Jun 08 2017

nonn

Robert Price, Table of n, a(n) for n = 1..29
Henri and Renaud Lifchitz, PRP Records.Search for n!10+2.
Joe McLean, Interesting Sources of Probable Primes.
OpenPFGW Project, Primality Tester.

Cf. A204657, A288327.

MultiFactorial[n_, k_] := If[n<1, 1, n*MultiFactorial[n-k, k]];
Select[Table[MultiFactorial[i, 10] + 2, {i, 0, 100}], PrimeQ[#]&]
Select[Table[Times@@Range[n,1,-10]+2,{n,200}],PrimeQ] (* Harvey P. Dale, May 26 2025 *)

a(n) = 2 + A288327(A204657(n+1)). - Elmo R. Oliveira, Feb 26 2025

cp's OEIS Frontend

A283559 Numbers k such that k![10]-2 is prime, where k![10] is the ten-fold multifactorial.

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A283594 Numbers k such that k![12]+2 is prime, where k![12] is the twelve-fold multifactorial.

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A287207 Numbers k such that k![6] + 2 is prime, where k![6] = A085158(k) = sextuple factorial.

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A288370 Primes of the form k!10 + 2, where k!10 is the decuple factorial number (A288327).

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Programs

Mathematica

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