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 18 results. Next

A084437 Duplicate of A037083.

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
Offset: 1

Views

Author

Keywords

A037082 Primes of the form k!!! + 1.

Original entry on oeis.org

2, 3, 5, 11, 19, 29, 163, 281, 881, 209441, 264539521, 72642169601, 9927882482918401, 26582634158080001, 141383412854531380076544001, 427380210218181008588800001, 2295148179742698933452800001, 191433282535027132859721811688265047080960000001
Offset: 1

Views

Author

G. L. Honaker, Jr.

Keywords

Examples

			11!!! + 1 = 11*8*5*2 + 1 = 881 is prime.

Links

Crossrefs

Cf. A007661, A037083.

Programs

  • Mathematica
    Select[Table[Times@@Range[n,1,-3]+1,{n,60}],PrimeQ] (* Harvey P. Dale, Jul 09 2014 *)

Formula

a(n) = 1 + A007661(A037083(n+1)). - Elmo R. Oliveira, Feb 22 2025

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

A204657 Numbers n such that n!10 + 2 is prime.

Original entry on oeis.org

0, 1, 3, 5, 9, 11, 13, 19, 21, 25, 41, 57, 79, 127, 135, 149, 165, 177, 193, 209, 223, 255, 273, 287, 297, 375, 433, 459, 481, 565, 1079, 1435, 1543, 1771, 1913, 1983, 2063, 2305, 2653, 6789, 8757, 11149, 13671, 15433, 16369, 17261, 18129, 22129, 22785, 22875, 25235, 25247, 26329, 27675, 33391, 39075, 41195, 47435, 47621, 48409, 59235, 59715, 61571, 65433, 78761, 83033
Offset: 1

Views

Author

M. F. Hasler, Jan 17 2012

Keywords

Comments

n!10 = Product_{k=0..floor((n-1)/10)}(n - 10k).
a(61) > 50000. - Robert Price, Jun 10 2012
The first 11 primes associated with this sequence: 3, 3, 5, 7, 11, 13, 41, 173, 233, 1877, 293603. - Robert Price, Mar 10 2017
a(67) > 10^5. - Robert Price, Mar 31 2017

Links

Crossrefs

Cf. A204658, A204659, A204660, A204661, A204662, A204663, A204664, A156165, A156167, A085150, A085148, A085146, A037083, A080778, A002981.

Programs

  • Mathematica
    MultiFactorial[n_, k_] := If[n < 1, 1, n*MultiFactorial[n - k, k]];
Select[Range[0, 50000], PrimeQ[MultiFactorial[#, 10] + 2] &]
  • PARI
    for(n=0,9999,isprime(prod(i=0,(n-2)\10,n-10*i)+2)& print1(n","))

Extensions

a(40)-a(59) from Robert Price, Jun 10 2012
Inserted missing term of 6789 by Robert Price, Mar 10 2017
a(61)-a(66) from Robert Price, Mar 31 2017

A156165 Numbers k such that k![7]+1 is prime (n![7] = A114799(n) = septuple factorial).

Original entry on oeis.org

0, 1, 2, 4, 6, 9, 10, 12, 13, 24, 25, 26, 29, 31, 35, 36, 47, 49, 57, 58, 64, 71, 73, 75, 78, 80, 97, 123, 125, 129, 131, 135, 147, 150, 159, 183, 201, 250, 251, 255, 298, 336, 337, 458, 467, 556, 570, 657, 743, 801, 908, 925, 1003, 1209, 1473, 1524, 1716, 1881, 1926
Offset: 1

Views

Author

M. F. Hasler, Feb 10 2009

Keywords

Comments

a(103) > 50000. - Robert Price, Sep 03 2012

Links

Crossrefs

Cf. A156167, A085150, A085148, A085146, A037083, A080778, A002981.

Programs

  • Mathematica
    mf[n_, k_] := Product[n - i k, {i, 0, Quotient[n - 2, k]}];
Reap[For[k = 0, k <= 2000, k++, If[PrimeQ[mf[k, 7] + 1], Sow[k]]]][[2, 1]] (* Jean-François Alcover, Feb 26 2019 *)
Select[Range[0,2000],PrimeQ[Times@@Range[#,1,-7]+1]&] (* Harvey P. Dale, Aug 21 2021 *)
  • PARI
    mf(n,k=7)=prod(i=0,(n-2)\k,n-i*k)
for( n=0,9999, ispseudoprime(mf(n)+1) & print1(n","))

A204659 Numbers n such that n!9-1 is prime.

Original entry on oeis.org

3, 4, 6, 8, 15, 20, 23, 27, 30, 44, 51, 62, 80, 90, 95, 114, 129, 138, 150, 152, 156, 182, 201, 216, 293, 332, 342, 393, 411, 414, 419, 525, 668, 743, 800, 972, 1034, 1266, 1785, 1869, 2777, 3561, 3780, 4106, 4328, 4428, 4556, 4574, 4629, 5001, 5397, 6315
Offset: 1

Views

Author

M. F. Hasler, Jan 17 2012

Keywords

Comments

n!9 = A114806(n).
a(74) > 50000. - Robert Price, Jun 14 2012
a(1)-a(73) are proved prime by the deterministic test of pfgw. - Robert Price, Jun 14 2012

Links

Crossrefs

Cf. A204657, A204658, A204660, A204661, A204662, A204663, A204664, A156165, A156167, A085150, A085148, A085146, A037083, A080778, A002981.

Programs

  • Mathematica
    MultiFactorial[n_, k_] := If[n < 1, 1, n*MultiFactorial[n - k, k]];
Select[Range[1000], PrimeQ[MultiFactorial[#, 9] - 1] & ] (* Robert Price, Apr 19 2019 *)
  • PARI
    for(n=0,9999,isprime(prod(i=0,(n-2)\9,n-9*i)-1)& print1(n","))

Extensions

a(47)-a(73) from Robert Price, Jun 14 2012
Extended b-file adding a(74)-a(81) using data from Ken Davis link by Robert Price, Apr 19 2019

A204660 Numbers n such that n!9+1 is prime.

Original entry on oeis.org

0, 1, 2, 4, 6, 10, 11, 12, 13, 14, 16, 17, 18, 19, 21, 24, 25, 32, 40, 43, 48, 49, 50, 57, 60, 71, 73, 82, 83, 86, 97, 105, 114, 121, 142, 147, 159, 168, 195, 205, 210, 212, 233, 262, 288, 289, 300, 309, 316, 323, 356, 403, 447, 505, 514, 553, 735, 739, 777
Offset: 1

Views

Author

M. F. Hasler, Jan 17 2012

Keywords

Comments

n!9 = A114806(n).
a(107) > 50000. - Robert Price, Jun 18 2012
a(1)-a(106) verified prime by deterministic test of PFGW. - Robert Price, Jun 18 2012

Links

Crossrefs

Cf. A204657, A204658, A204659, A204661, A204662, A204663, A204664, A156165, A156167, A085150, A085148, A085146, A037083, A080778, A002981.

Programs

  • Mathematica
    MultiFactorial[n_, k_] := If[n < 1, 1, n*MultiFactorial[n - k, k]];
Select[Range[0, 1000], PrimeQ[MultiFactorial[#, 9] + 1] & ] (* Robert Price, Apr 19 2019 *)
Select[Range[0,800],PrimeQ[Times@@Range[#,1,-9]+1]&] (* Harvey P. Dale, Aug 19 2021 *)
  • PARI
    for(n=0,9999,isprime(prod(i=0,(n-2)\9,n-9*i)+1)& print1(n","))

A204658 Numbers n such that n!10-1 is prime.

Original entry on oeis.org

3, 4, 6, 8, 12, 20, 40, 48, 60, 62, 70, 84, 88, 168, 240, 258, 372, 760, 932, 1010, 2110, 2464, 2490, 2702, 3180, 4744, 6024, 8858, 9060, 10322, 13382, 15778, 19322, 22372, 22928, 25344, 28050, 40604, 42282, 45884, 52428, 58250, 81220, 93612, 108650
Offset: 1

Views

Author

M. F. Hasler, Jan 17 2012

Keywords

Comments

n!10 = product( n-10k, 0 <= k < n/10 ).
See also links in A156165.
a(1)-a(40) are proved prime by deterministic tests of pfgw. - Robert Price, Jun 11 2012
a(41) > 50000. - Robert Price, Jun 11 2012

Links

Crossrefs

Cf. A204657, A204659, A204660, A204661, A204662, A204663, A204664, A156165, A156167, A085150, A085148, A085146, A037083, A080778, A002981.

Programs

  • Mathematica
    MultiFactorial[n_, k_] := If[n < 1, 1, n*MultiFactorial[n - k, k]];
Select[Range[1000], PrimeQ[MultiFactorial[#, 10] - 1] & ] (* Robert Price, Apr 19 2019 *)
  • PARI
    for(n=0,9999,isprime(prod(i=0,(n-2)\10,n-10*i)-1)& print1(n","))

Extensions

a(26)-a(40) from Robert Price, Jun 11 2012
a(41)-a(45) from Ken Davis link entered by Robert Price, Apr 19 2019

A204661 Numbers n such that n!8+1 is prime (for n!8 see A114800).

Original entry on oeis.org

0, 1, 2, 4, 6, 28, 30, 46, 60, 72, 86, 90, 112, 154, 162, 206, 280, 354, 400, 512, 606, 614, 678, 790, 938, 1054, 1092, 1148, 1582, 1788, 2088, 2206, 2598, 2912, 3672, 4642, 6272, 6428, 7084, 7604, 8580, 9464, 12762, 18386, 24910, 30448, 31696, 40288, 41682, 45730
Offset: 1

Views

Author

M. F. Hasler, Jan 17 2012

Keywords

Comments

n!8 = A114800(n).
No other terms < 50000. - Robert Price, Jul 29 2012

Links

Crossrefs

Cf. A204657, A204658, A204659, A204660, A204662, A204663, A204664, A156165, A156167, A085150, A085148, A085146, A037083, A080778, A002981.

Programs

  • Mathematica
    MultiFactorial[n_, k_] := If[n < 1, 1, n*MultiFactorial[n - k, k]];
Select[Range[0, 1000], PrimeQ[MultiFactorial[#, 8] + 1] & ] (* Robert Price, Apr 19 2019 *)
Select[Range[0,46000],PrimeQ[Times@@Range[#,1,-8]+1]&] (* Harvey P. Dale, Apr 12 2022 *)
  • PARI
    for(n=0,9999,isprime(prod(i=0,(n-2)\8,n-8*i)+1)& print1(n","))

Extensions

a(35)-a(50) from Robert Price, Jul 29 2012

A204662 Numbers n such that n!8-1 is prime.

Original entry on oeis.org

3, 4, 6, 8, 10, 12, 14, 16, 18, 22, 28, 30, 42, 48, 58, 68, 80, 86, 92, 108, 110, 112, 130, 198, 220, 230, 322, 432, 460, 478, 686, 706, 714, 842, 950, 1010, 1090, 1314, 1904, 2264, 2804, 3164, 3324, 4740, 4824, 4918, 5086, 5442, 6994, 7898, 8236, 8684, 10088, 13990, 15320, 17570, 18218, 21564, 22198, 22684, 24314, 24780, 25790, 38726
Offset: 1

Views

Author

M. F. Hasler, Jan 17 2012

Keywords

Comments

n!8 = A114800(n).
No other terms < 50000. - Robert Price, Aug 15 2012

Links

Crossrefs

Cf. A204657, A204658, A204659, A204660, A204661, A204663, A204664, A156165, A156167, A085150, A085148, A085146, A037083, A080778, A002981.

Programs

  • Mathematica
    MultiFactorial[n_, k_] := If[n < 1, 1, n*MultiFactorial[n - k, k]];
Select[Range[0, 1000], PrimeQ[MultiFactorial[#, 8] - 1] & ] (* Robert Price, Apr 19 2019 *)
  • PARI
    for(n=0,9999,isprime(prod(i=0,(n-2)\8,n-8*i)-1)& print1(n","))

Extensions

a(39)-a(64) from Robert Price, Aug 15 2012
Showing 1-10 of 18 results. Next

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

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