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 1-10 of 59 results. Next

A242994 Numbers n such that n!3 - 3 is prime, where n!3 = n!!! is a triple factorial number (A007661).

Original entry on oeis.org

5, 10, 11, 13, 16, 22, 28, 71, 74, 94, 119, 121, 134, 157, 200, 262, 286, 484, 1039, 1045, 1190, 1595, 1679, 1772, 1789, 2410, 2920, 5039, 7919, 10462, 11846, 23293, 26705, 30781, 43694
Offset: 1

Views

Author

Robert Price, Aug 17 2014

Keywords

Comments

Large terms correspond to probable primes. - Jens Kruse Andersen, Aug 19 2014
a(36) > 50000. - Robert Price, Oct 12 2014

Examples

			11!3-3 = 11*8*5*2-3 = 877 is prime, so 11 is in the sequence. - _Jens Kruse Andersen_, Aug 19 2014

Links

Crossrefs

Cf. A007661, A037082, A084438, A243078.

Programs

  • Mathematica
    MultiFactorial[n_, k_] := If[n < 1, 1, If[n < k + 1, n, n*MultiFactorial[n - k, k]]];
lst={};Do[If[PrimeQ[MultiFactorial[n, 3] - 3], AppendTo[lst, n]], {n, 100}];lst

Extensions

Links and crossrefs fixed by Jens Kruse Andersen, Aug 19 2014
a(35) from Robert Price, Oct 12 2014

A037083 Numbers k such that k!!! + 1 is prime (0 is included by convention).

Original entry on oeis.org

0, 1, 2, 4, 5, 6, 7, 9, 10, 11, 17, 24, 29, 39, 40, 57, 58, 59, 91, 155, 175, 245, 359, 372, 597, 864, 977, 1077, 1327, 2076, 4798, 4975, 10830, 13453, 15472, 15948, 16116, 16681, 18037, 21725, 22326, 24753, 28565, 32659, 46487, 50649, 51393, 80069, 95493
Offset: 1

Views

Author

G. L. Honaker, Jr.

Keywords

Comments

n!!! = n*(n-3)*(n-6)*(n-9)*...
The search for multifactorial primes started by Ray Ballinger is now continued by a team of volunteers on the website of Ken Davis (see link).

Links

Crossrefs

Cf. A007661 (triple factorials), A084438, A037082.

Extensions

More terms from Steven Harvey
Corrected and extended by Hugo Pfoertner, Jun 25 2003
More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 03 2008
Edited by N. J. A. Sloane, Jan 14 2008

A243078 Numbers k such that k!3 - 3^2 is prime, where k!3 = k!!! is a triple factorial number (A007661).

Original entry on oeis.org

7, 8, 10, 13, 16, 17, 20, 23, 28, 29, 32, 43, 46, 47, 53, 56, 59, 61, 76, 95, 107, 139, 148, 218, 349, 764, 1009, 1130, 1183, 1429, 1516, 2072, 2471, 4937, 10204, 13993, 16249, 18166, 25733, 29033, 40090
Offset: 1

Views

Author

Robert Price, May 30 2014

Keywords

Comments

a(42) > 50000.
k=2 and k=4 produce values (-7 and -5) whose absolute value is a prime.
Terms > 2000 correspond to probable primes.

Examples

			17!3 - 3^2 = 17*14*11*8*5*2 - 9 = 209431 is prime, so 17 is in the sequence. - _Jens Kruse Andersen_, Aug 20 2014

Links

Crossrefs

Cf. A007661, A037082, A084438, A123910, A242994.

Programs

  • Mathematica
    MultiFactorial[n_,k_]:=If[n<1,1,If[n

Extensions

a(41) from Robert Price, Sep 19 2014

A156167 Numbers n such that n![7]-1 is prime (where n![7] = A114799(n) = septuple factorial).

Original entry on oeis.org

3, 4, 6, 8, 9, 10, 11, 12, 14, 17, 20, 24, 30, 31, 32, 46, 52, 54, 59, 98, 104, 143, 145, 160, 174, 198, 199, 202, 212, 215, 254, 371, 382, 452, 674, 739, 959, 1249, 1657, 2291, 2553, 2650, 3562, 3727, 3853, 4389, 4604, 5449, 5659, 6026, 6878, 7900, 9564, 10150, 12444, 13321, 22642, 24014, 26598, 27430, 31386, 40707, 43328, 45811
Offset: 1

Views

Author

M. F. Hasler, Feb 10 2009

Keywords

Comments

a(65) > 50000. - Robert Price, Sep 09 2012

Links

Crossrefs

cf. A156165, A051592, A085149, A085147, A084438, A007749, A002982.

Programs

  • Mathematica
    MultiFactorial[n_, k_] := If[n < 1, 1, n*MultiFactorial[n - k, k]];
Select[Range[0, 1000], PrimeQ[MultiFactorial[#, 7] - 1] & ] (* Robert Price, Apr 19 2019 *)
  • PARI
    mf(n,k=7)=prod(i=0,(n-2)\k,n-i*k)
for( n=1,9999, ispseudoprime(mf(n)-1) & print1(n","))

Extensions

a(43)-a(64) from Robert Price, Sep 09 2012

A261145 Numbers n such that n!3 + 3^10 is prime, where n!3 = n!!! is a triple factorial number (A007661).

Original entry on oeis.org

2, 4, 7, 11, 25, 38, 47, 94, 95, 155, 275, 277, 292, 299, 395, 409, 614, 1409, 1963, 3422, 5243, 5884, 5971, 8527, 10882, 13223, 16406, 20851, 28886
Offset: 1

Views

Author

Robert Price, Nov 18 2015

Keywords

Comments

Corresponding primes are: 59051, 59053, 59077, 59929, 608667049, 3091650738235049, 262134882788466747049, ...
a(30) > 50000.
Terms > 47 correspond to probable primes.

Examples

			11!3 + 3^10 = 11*8*5*2 + 59049 = 59929 is prime, so 11 is in the sequence.

Links

Crossrefs

Cf. A007661, A037082, A084438, A123910, A242994.

Programs

  • Mathematica
    MultiFactorial[n_, k_] := If[n < 1, 1, If[n < k + 1, n, n*MultiFactorial[n - k, k]]];
Select[Range[0, 50000], PrimeQ[MultiFactorial[#, 3] + 3^10] &]
  • PARI
    for(n=1, 1e3, if(ispseudoprime(prod(i=0, floor((n-1)/3), n-3*i) + 3^10), print1(n, ", "))) \\ Altug Alkan, Nov 18 2015

A135726 Primes of the form k!!! - 1 = A007661(k) - 1, k > 0.

Original entry on oeis.org

2, 3, 17, 79, 4188799, 2504902399, 254561089305599, 13106744139423334399999, 8483004771271882804592639999, 706526001186582385898210420541078864497278132689882316799999999, 353401447088718405944982176443380974931403135679741865504466985287679999999999
Offset: 1

Views

Author

M. F. Hasler, Nov 26 2007

Keywords

Comments

Sequence A084438 gives the easier-to-read n-values.
All terms greater than a(3) seem to end in the digit 9, or many 9 digits. a(17) ends with 51 9 digits. - Harvey P. Dale, Nov 28 2019

Examples

			a(4) = 79 = 8*5*2 - 1 = 8!!! - 1 is the 4th prime of that form.

Links

Crossrefs

Cf. A007661, A037082, A037083, A084438.

Programs

  • Mathematica
    Select[Table[Times@@Range[n,1,-3],{n,150}]-1,PrimeQ] (* Harvey P. Dale, Nov 28 2019 *)
  • PARI
    A007661(n) = prod(i=1,(n-1)\3,n-=3,n+!n)
for(n=1,999,if(isprime(A007661(n)-1),print1(A007661(n)-1,",")))

Formula

a(n) = A007661(A084438(n)) - 1. - Elmo R. Oliveira, Feb 25 2025

A265200 Numbers n such that n!3 + 3^7 is prime, where n!3 = n!!! is a triple factorial number (A007661).

Original entry on oeis.org

8, 10, 11, 13, 16, 19, 20, 22, 37, 38, 47, 73, 92, 94, 100, 218, 241, 284, 482, 541, 736, 787, 829, 916, 1147, 1312, 1856, 1928, 2035, 3134, 4958, 5503, 8042, 16898, 16987, 24548, 25076, 35086
Offset: 1

Views

Author

Robert Price, Dec 04 2015

Keywords

Comments

Corresponding primes are: 2267, 2467, 3067, 5827, 60427, 1108747, 4190987, 24346507, 664565853954187, ...
a(39) > 50000.
Terms > 38 correspond to probable primes.

Examples

			11!3 + 3^7 = 11*8*5*2 + 2187 = 3067 is prime, so 11 is in the sequence.

Links

Crossrefs

Cf. A007661, A037082, A084438, A123910, A242994, A261145.

Programs

  • Mathematica
    MultiFactorial[n_, k_] := If[n < 1, 1, If[n < k + 1, n, n*MultiFactorial[n - k, k]]];
Select[Range[0, 50000], PrimeQ[MultiFactorial[#, 3] + 3^7] &]
Select[Range[35100],PrimeQ[Times@@Range[#,1,-3]+2187]&] (* Harvey P. Dale, Oct 19 2023 *)
  • PARI
    tf(n) = prod(i=0, (n-1)\3, n-3*i);
for(n=1, 1e4, if(ispseudoprime(tf(n) + 3^7), print1(n , ", "))) \\ Altug Alkan, Dec 04 2015

A247463 Numbers n such that n!3 - 3^3 is prime, where n!3 = n!!! is a triple factorial number (A007661).

Original entry on oeis.org

8, 11, 13, 22, 29, 49, 56, 61, 103, 142, 149, 257, 319, 365, 680, 736, 737, 749, 947, 974, 1040, 4277, 4678, 9961, 10652, 15545, 18064, 31325, 34918, 41032
Offset: 1

Views

Author

Robert Price, Sep 17 2014

Keywords

Comments

Large terms correspond to probable primes.
a(31) > 50000.

Examples

			11!3-27 = 11*8*5*2-27 = 853 is prime, so 11 is in the sequence.

Links

Crossrefs

Cf. A007661, A037082, A084438, A243078.

Programs

  • Mathematica
    MultiFactorial[n_, k_] := If[n < 1, 1, If[n < k + 1, n, n*MultiFactorial[n - k, k]]];
lst={};Do[If[PrimeQ[MultiFactorial[n, 3] - 27], AppendTo[lst, n]], {n, 100}];lst
Select[Range[6,1100],PrimeQ[Times@@Range[#,1,-3]-27]&] (* Harvey P. Dale, Mar 16 2023 *)

A247464 Numbers n such that n!!! - 3^4 is prime.

Original entry on oeis.org

10, 13, 14, 17, 20, 26, 29, 31, 32, 50, 59, 77, 82, 104, 164, 185, 217, 263, 293, 361, 437, 442, 545, 547, 599, 608, 623, 739, 782, 1081, 1120, 1138, 1429, 2516, 2518, 4277, 4529, 5438, 5596, 11945, 12716, 13955, 14540, 31730, 31769, 42964, 46396
Offset: 1

Views

Author

Robert Price, Sep 17 2014

Keywords

Comments

Large terms correspond to probable primes.
a(48) > 50000.

Examples

			10!3-81 = 10*7*4*1-81 = 199 is prime, so 10 is in the sequence.

Links

Crossrefs

Cf. A007661, A037082, A084438, A243078.

Programs

  • Mathematica
    MultiFactorial[n_, k_] := If[n < 1, 1, If[n < k + 1, n, n*MultiFactorial[n - k, k]]];
lst={};Do[If[PrimeQ[MultiFactorial[n, 3] - 81], AppendTo[lst, n]], {n, 100}];lst

A247465 Numbers n such that n!3 - 3^5 is prime.

Original entry on oeis.org

10, 19, 28, 50, 67, 77, 89, 112, 139, 146, 184, 194, 233, 310, 311, 388, 886, 1139, 1648, 1694, 2405, 2554, 3709, 4015, 5410, 5908, 6407, 8065, 9061, 9875, 11722, 13471, 26026, 26656, 29441, 32741
Offset: 1

Views

Author

Robert Price, Sep 17 2014

Keywords

Comments

Large terms correspond to probable primes.
a(37) > 50000.

Examples

			10!3-243 = 10*7*4*1-243 = 37 is prime, so 10 is in the sequence.

Links

Crossrefs

Cf. A007661, A037082, A084438, A243078.

Programs

  • Mathematica
    MultiFactorial[n_, k_] := If[n < 1, 1, If[n < k + 1, n, n*MultiFactorial[n - k, k]]];
lst={};Do[If[PrimeQ[MultiFactorial[n, 3] - 243], AppendTo[lst, n]], {n, 100}];lst
Showing 1-10 of 59 results. Next

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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