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.

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A076197 Numbers k such that k!! + 2^10 is prime.

Original entry on oeis.org

5, 7, 21, 33, 153, 167, 171, 391, 789, 1323, 2645, 8655, 10153, 39967, 45369, 47599
Offset: 1

Views

Author

Zak Seidov, Nov 02 2002

Keywords

Comments

a(17) > 50000. - Robert Price, Feb 24 2015

Links

Crossrefs

Cf. A006882.
Numbers k such that k!! + 2^s is prime: A080778 (s=0), A076185 (s=1), A076186 (s=2), A076188 (s=3), A076189 (s=4), A076190 (s=5), A076193 (s=6), A076194 (s=7), A076195 (s=8), A076196 (s=9).

Programs

  • Mathematica
    lst={};Do[If[PrimeQ[n!!+2^10], (*Print[n];*)AppendTo[lst, n]], {n, 6!}];lst (* Vladimir Joseph Stephan Orlovsky, Aug 26 2008 *)
  • Python
    from gmpy2 import is_prime
A076197_list, g, h = [], 1, 1024
for i in range(3,10**5,2):
    g *= i
    if is_prime(g+h):
        A076197_list.append(i) # Chai Wah Wu, May 31 2015

Extensions

Edited and extended (n<4096) by Hugo Pfoertner, Jun 19 2003
8655 from Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 03 2008
a(13) from Robert Price, Mar 10 2013
a(14)-a(16) from Robert Price, Feb 24 2015

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

A204663 Numbers n such that n!8 + 2 is prime.

Original entry on oeis.org

0, 1, 3, 5, 9, 13, 15, 21, 23, 27, 33, 35, 45, 53, 55, 57, 75, 79, 109, 197, 221, 227, 267, 333, 413, 545, 695, 703, 801, 967, 1029, 1329, 1351, 1475, 1549, 1757, 2173, 2861, 3161, 3167, 3885, 4681, 4965, 6277, 6655, 8477, 9821, 9959, 10269, 17999, 23349, 29347, 29477, 30181, 34133, 36687, 40985, 43395, 47499
Offset: 1

Views

Author

M. F. Hasler, Jan 17 2012

Keywords

Comments

n!8 = A114800(n).
See also links in A156165.
For odd k, n!k +-2 is even for all n > k and thus cannot be prime.
a(60) > 50000. - Robert Price, Aug 19 2012

Links

Crossrefs

Cf. A204657, A204658, A204659, A204660, A204661, A204662, A204664, A156165, A156167, A085150, A085148, A085146, A037083, A080778, A002981.

Programs

  • Mathematica
    Select[Range[0,9999], PrimeQ[Product[# - 8i,{i, 0, Floor[(# - 2)/8]}] + 2] &] (* Indranil Ghosh, Mar 13 2017 *)
  • PARI
    for(n=0,9999,isprime(prod(i=0,(n-2)\8,n-8*i)+2)& print1(n","))

Extensions

a(39)-a(59) from Robert Price, Aug 19 2012

A204664 Numbers n such that n!8-2 is prime.

Original entry on oeis.org

4, 5, 7, 9, 11, 15, 17, 25, 27, 33, 47, 59, 63, 77, 87, 89, 93, 95, 107, 119, 127, 133, 139, 193, 201, 217, 269, 291, 369, 373, 435, 445, 669, 803, 831, 859, 907, 1271, 1705, 1743, 1849, 3087, 3189, 3497, 4221, 4475, 5119, 6013, 8023, 9237, 12755, 16501, 16747, 17021, 17309, 20671, 21539, 28377, 33625, 35645, 36831, 54663, 56223, 65299, 66159, 68121, 69339, 70579, 73511, 77745, 94601
Offset: 1

Views

Author

M. F. Hasler, Jan 17 2012

Keywords

Comments

n!8 = A114800(n).
See also links in A156165.
For odd k, n!k +- 2 is even for all n > k and thus cannot be prime.
a(62) > 50000. - Robert Price, Aug 27 2012
The first 10 associated primes: 2, 3, 5, 7, 31, 103, 151, 3823, 16927, 126223. - Robert Price, Mar 10 2017
a(72) > 10^5. - Robert Price, Apr 24 2017

Links

Crossrefs

Cf. A204657, A204658, A204659, A204660, A204661, A204662, A204663, A156165, A156167, A085150, A085148, A085146, A037083, A080778, A002981.

Programs

  • Mathematica
    MultiFactorial[n_, k_] := If[n < 1, 1, n*MultiFactorial[n - k, k]];
Select[Range[4, 50000], PrimeQ[MultiFactorial[#, 8] - 2] &] (* Robert Price, Mar 10 2017 *)
  • PARI
    for(n=0,9999,isprime(prod(i=0,(n-2)\8,n-8*i)-2)& print1(n","))

Extensions

a(46)-a(61) from Robert Price, Aug 27 2012
a(62)-a(71) from Robert Price, Apr 24 2017

A256594 Numbers k such that k!*2^k + 1 is prime.

Original entry on oeis.org

0, 1, 259, 16708, 18655, 26304, 61999, 110251
Offset: 1

Views

Author

Robert Price, Apr 03 2015

Keywords

Examples

			0 is in the sequence since 0!*2^0 + 1 = 2 is prime.

Crossrefs

Cf. A007749, A080778, A117141, A091415.

Programs

  • Magma
    [n: n in [0..3*10^2] | IsPrime(Factorial(n)*2^n+1)]; // Vincenzo Librandi, Apr 05 2015
  • Mathematica
    Select[Range[0, 20000], PrimeQ[2^#*#! + 1] &]
  • PARI
    for(n=0,300,if(ispseudoprime(n!*2^n+1),print1(n,", "))) \\ Derek Orr, Apr 05 2015
  • Python
    from sympy import factorial, isprime
for n in range(0,300):
    if isprime(factorial(n)*(2**n)+1):
        print(n, end=', ') # Stefano Spezia, Dec 06 2018

Formula

a(n) = A080778(n+1)/2 for n >= 2. - Amiram Eldar, Dec 06 2018

Extensions

a(6)-a(8), from the data at A080778, added by Amiram Eldar, Dec 06 2018
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