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 118 results. Next

A084438 Positive integers k such that k!!! - 1 = A007661(k) - 1 is prime.

Original entry on oeis.org

3, 4, 6, 8, 20, 26, 36, 50, 60, 114, 135, 138, 248, 315, 351, 429, 642, 5505, 8793, 12086, 13580, 23109, 34626, 34706, 56282, 57675, 58298
Offset: 1

Views

Author

Hugo Pfoertner, Jun 25 2003

Keywords

Comments

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).

Examples

			a(4) = 8 since 8!!! - 1 = 8*5*2 - 1 = 79 is the 4th prime of that form.
26!!! - 1 = 2504902399 is prime.

Links

Crossrefs

Cf. A007661, A135726, A037082, A037083.

Programs

  • Mathematica
    multiFactorial[n_, k_] := If[n < 1, 1, n * multiFactorial[n - k, k]];
Select[Range[0, 1000], PrimeQ[multiFactorial[#, 3] - 1] & ] (* Robert Price, Apr 19 2019 *)
Select[Range[650], PrimeQ[Times @@ Range[#, 1, -3] - 1] &] (* The program generates the first 17 terms of the sequence. To generate more, change the Range constant but the program may take a long time to run. *) (* Harvey P. Dale, May 22 2021 *)
  • PARI
    A007661(n) = prod(i=1,(n-1)\3,n-=3,n+!n)
for(n=1,999,if(isprime(A007661(n)-1),print1(n","))) \\ M. F. Hasler, Nov 26 2007

Extensions

Missing 26 inserted by M. F. Hasler, Nov 26 2007
More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 03 2008
Edited by N. J. A. Sloane, Feb 11 2009 at the suggestion of M. F. Hasler

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

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

A114347 Cumulative sum of triple factorial numbers a(n) = n!!! (A007661).

Original entry on oeis.org

1, 2, 4, 7, 11, 21, 39, 67, 147, 309, 589, 1469, 3413, 7053, 19373, 48533, 106773, 316213, 841093, 1947653, 6136453, 17158933, 41503253, 137845653, 402385173, 1010993173, 3515895573, 10658462613, 27699486613, 100341656213, 314618667413, 842890411413
Offset: 0

Views

Author

Jonathan Vos Post, Feb 08 2006

Keywords

Comments

Triple factorial numbers n!!! = n*(n-3)!!!, 0!!! = 1!!! = 1, 2!!! = 2.
The cumulative sum a(n) is prime for n = 1, 3, 4, 7, 12, 14, 15, 17, 19.
The cumulative sum a(n) is semiprime for n = 2, 5, 6, 9, 10, 11, 13, 16, 18, 20, 22, 26, 28, 29.

Examples

			a(29) = 1 + 1 + 2 + 3 + 4 + 10 + 18 + 28 + 80 + 162 + 280 + 880 + 1944 + 3640 + 12320 + 29160 + 58240 + 209440 + 524880 + 1106560 + 4188800 + 11022480 + 24344320 + 96342400 + 264539520 + 608608000 + 2504902400 + 7142567040 + 17041024000 + 726421696 = 100341656213 = 79 * 1270147547.

References

  • J. Spanier and K. B. Oldham, An Atlas of Functions, Hemisphere, NY, 1987, p. 23.

Links

Crossrefs

Cf. A000040, A001358, A007661.

Formula

a(n) = Sum_{i=0..n} i!!!.
a(n) = Sum_{i=0..n} A007661(i).

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

A265201 Numbers n such that n!!! - 3^10 is prime, where n!3 = n!!! is a triple factorial number (A007661).

Original entry on oeis.org

19, 20, 22, 26, 41, 55, 56, 152, 155, 316, 347, 383, 500, 556, 646, 656, 748, 976, 1433, 2213, 2680, 2911, 3373, 4799, 4964, 7189, 8798, 9871, 14069, 14627, 16657, 20230, 24137, 24430, 28331, 36313, 41522, 43031, 46072, 47719
Offset: 1

Views

Author

Robert Price, Dec 04 2015

Keywords

Comments

Corresponding primes are 1047511, 4129751, 24285271, 2504843351, 126757680265156951, ... .
a(41) > 50000.

Examples

			19!3 - 3^10 = 19*16*13*10*7*4*1 - 59049 = 1047511 is prime, so 19 is in the sequence.

Links

Crossrefs

Cf. A006882, A007749, A094144, A123910, A258452, A258616, A262772, A261145.

Programs

  • Mathematica
    MultiFactorial[n_, k_] := If[n < 1, 1, If[n < k + 1, n, n*MultiFactorial[n - k, k]]];
Select[Range[17, 50000], PrimeQ[MultiFactorial[#, 3] - 3^10] &]
  • PARI
    tf(n) = prod(i=0, (n-1)\3, n-3*i);
for(n=1, 1e4, if(ispseudoprime(tf(n) - 3^10), print1(n , ", "))) \\ Altug Alkan, Dec 04 2015

A045767 Number of prime factors of triple factorials n!!! (A007661), with multiplicity.

Original entry on oeis.org

0, 1, 1, 2, 2, 3, 3, 5, 5, 5, 6, 8, 6, 8, 10, 10, 9, 13, 11, 12, 15, 13, 13, 19, 15, 15, 22, 18, 16, 25, 19, 21, 27, 21, 23, 31, 22, 25, 33, 26, 26, 36, 27, 29, 39, 29, 30, 44, 31, 33, 46, 34, 34, 50, 36, 38, 52, 38, 39, 56, 39, 41, 59, 45, 43, 62, 46, 46, 64, 49, 47, 69, 50, 49
Offset: 1

Views

Author

Jeff Burch

Keywords

Links

Programs

  • Mathematica
    Rest[PrimeOmega/@RecurrenceTable[{a[0]==a[1]==1,a[2]==2,a[n]==n*a[n-3]},a,{n,80}]] (* Harvey P. Dale, May 17 2012 *)
Table[PrimeOmega[Times@@Range[n,1,-3]],{n,80}] (* Harvey P. Dale, Apr 11 2020 *)

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 *)
Showing 1-10 of 118 results. Next

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

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