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 1-8 of 8 results.

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

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

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

A288716 Primes of the form k!8+2, where k!8 is the octuple factorial number (A114800).

Original entry on oeis.org

3, 5, 7, 11, 67, 107, 1367, 2417, 16931, 126227, 592517, 65909027, 3493178327, 7547514977, 14454403427, 385235284982627, 2667042724170827, 98523573068265783062627, 121598818552526868243555286516922298627484453127
Offset: 1

Views

Author

Robert Price, Jun 13 2017

Keywords

Links

Crossrefs

Cf. A204663.

Programs

  • Mathematica
    MultiFactorial[n_, k_] := If[n<1, 1, n*MultiFactorial[n-k, k]];
Select[Table[MultiFactorial[i, 8] + 2, {i, 0, 100}], PrimeQ[#]&]
Showing 1-8 of 8 results.

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