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 26 results. Next

A124178 Numbers n such that 1 + n + n^3 + n^5 + n^7 + n^9 + n^11 + n^13 + n^15 + n^17 + n^19 is prime.

Original entry on oeis.org

1, 3, 6, 33, 36, 61, 70, 99, 168, 229, 267, 268, 321, 325, 337, 366, 387, 448, 456, 457, 498, 513, 532, 546, 591, 621, 624, 637, 835, 858, 910, 927, 961, 981, 1045, 1125, 1213, 1237, 1242, 1257, 1341, 1357, 1437, 1458, 1461, 1462, 1482, 1491, 1572, 1579, 1581
Offset: 1

Views

Author

Artur Jasinski, Dec 13 2006

Keywords

Links

Crossrefs

Cf. A049407, similar sequences listed in A244376.

Programs

  • Magma
    [n: n in [0..2000] | IsPrime(1 +n +n^3 +n^5 +n^7 +n^9 +n^11 +n^13 +n^15 +n^17 +n^19)]; // Vincenzo Librandi, Nov 12 2010
  • Magma
    [n: n in [0..2000] | IsPrime(s) where s is 1+&+[n^i: i in [1..19 by 2]]]; // Vincenzo Librandi, Jun 28 2014
  • Mathematica
    Do[If[PrimeQ[1 + n + n^3 + n^5 + n^7 + n^9 + n^11 + n^13 + n^15 + n^17 + n^19], Print[n]], {n, 1, 1000}]
Select[Range[3000], PrimeQ[Total[#^Range[1, 19, 2]] + 1] &] (* Vincenzo Librandi, Jun 28 2014 *)
  • PARI
    is(n)=n==1 || isprime((n^21-n)/(n^2-1)+1) \\ Charles R Greathouse IV, Jul 02 2013
  • Sage
    i,n = var('i,n')
[n for n in (1..2000) if is_prime(1+(n^(2*i+1)).sum(i,0,9))] # Bruno Berselli, Jun 28 2014

A124181 Numbers n such that 1 + n + n^3 + n^5 + n^7 + n^9 + n^11 + n^13 + n^15 + n^17 + n^19 + n^21 + n^23 is prime.

Original entry on oeis.org

1, 3, 69, 86, 104, 110, 138, 146, 210, 238, 247, 260, 264, 269, 316, 436, 572, 600, 621, 654, 666, 715, 737, 740, 744, 754, 779, 1056, 1156, 1159, 1216, 1218, 1221, 1343, 1419, 1434, 1442, 1524, 1580, 1603, 1676, 1680, 1731, 1742, 1804, 1952, 1956, 1985
Offset: 1

Views

Author

Artur Jasinski, Dec 13 2006

Keywords

Links

Crossrefs

Cf. A049407, similar sequences listed in A244376.

Programs

  • Magma
    [n: n in [0..2000] | IsPrime(s) where s is 1+&+[n^i: i in [1..23 by 2]]]; // Vincenzo Librandi, Jun 28 2014
  • Mathematica
    Do[If[PrimeQ[1 + n + n^3 + n^5 + n^7 + n^9 + n^11 + n^13 + n^15 + n^17 + n^19 + n^21 + n^23], Print[n]], {n, 1, 1400}]
Select[Range[3000], PrimeQ[Total[#^Range[1, 23, 2]] + 1] &] (* Vincenzo Librandi, Jun 28 2014 *)
  • PARI
    is(n)=n==1 || isprime((n^25-n)/(n^2-1)+1) \\ Charles R Greathouse IV, Jul 02 2013
  • Sage
    i,n = var('i,n')
[n for n in (1..2000) if is_prime(1+(n^(2*i+1)).sum(i,0,11))] # Bruno Berselli, Jun 27 2014

Formula

1 together with numbers n such that (n^25-n)/(n^2-1) + 1 is prime. - Charles R Greathouse IV, Jul 02 2013

A124154 Numbers n such that 1 + n + n^3 + n^5 is prime.

Original entry on oeis.org

2, 4, 8, 20, 22, 32, 36, 50, 54, 62, 64, 72, 78, 84, 86, 90, 92, 94, 96, 98, 112, 124, 134, 144, 146, 216, 224, 238, 240, 246, 250, 256, 262, 276, 294, 296, 298, 300, 314, 334, 370, 378, 382, 392, 400, 402, 406, 420, 430, 450, 472, 480, 482, 494, 510, 512, 526
Offset: 1

Views

Author

Artur Jasinski, Dec 13 2006

Keywords

Comments

All numbers n have to be even, because sum of 3 odd + 1 is even and can't be prime >3.

Links

Crossrefs

Cf. A049407, similar sequences listed in A244376.

Programs

  • Magma
    [n: n in [0..600] | IsPrime(s) where s is 1+&+[n^i: i in [1..5 by 2]]]; // Vincenzo Librandi, Jun 27 2014
  • Mathematica
    Do[If[PrimeQ[1 + n + n^3 + n^5], Print[n]], {n, 1, 300}]
Select[Range[1000], PrimeQ[Total[#^Range[1, 5, 2]] + 1] &] (* Vincenzo Librandi, Jun 27 2014 *)
  • PARI
    forstep(n=2,1000,2,if(isprime(1 + n + n^3 + n^5), print1(n","))) \\ Franklin T. Adams-Watters, Apr 09 2009

Extensions

More terms from Franklin T. Adams-Watters, Apr 09 2009

A124163 Numbers n such that 1 + n + n^3 + n^5 + n^7 + n^9 is prime.

Original entry on oeis.org

2, 12, 14, 18, 48, 62, 80, 86, 116, 120, 138, 212, 230, 264, 272, 362, 368, 386, 392, 422, 440, 450, 456, 468, 480, 492, 510, 518, 528, 534, 548, 558, 620, 632, 678, 710, 744, 770, 780, 834, 884, 900, 918, 960, 1022, 1032, 1074, 1080, 1146, 1170, 1178, 1212, 1232, 1242, 1260, 1308, 1382, 1440, 1470, 1482, 1524
Offset: 1

Views

Author

Artur Jasinski, Dec 13 2006

Keywords

Links

Crossrefs

Cf. A049407, similar sequences listed in A244376.

Programs

  • Magma
    [n: n in [0..1500]| IsPrime(1 + n + n^3 + n^5 + n^7+ n^9 )]; // Vincenzo Librandi, Nov 13 2010
  • Magma
    [n: n in [0..1200] | IsPrime(s) where s is 1+&+[n^i: i in [1..9 by 2]]]; // Vincenzo Librandi, Jun 27 2014
  • Mathematica
    Do[If[PrimeQ[1 + n + n^3 + n^5 + n^7 + n^9], Print[n]], {n, 1, 300}]
Select[Range[2000], PrimeQ[Total[#^Range[1, 9, 2]] + 1] &] (* Vincenzo Librandi, Jun 27 2014 *)
  • PARI
    is(n)=isprime(1+n+n^3+n^5+n^7+n^9) \\ Charles R Greathouse IV, Feb 20 2017

A124164 Numbers n such that 1 + n + n^3 + n^5 + n^7 + n^9 + n^11 + n^13 is prime.

Original entry on oeis.org

10, 30, 52, 70, 94, 120, 126, 142, 150, 160, 292, 318, 336, 378, 466, 792, 918, 960, 1044, 1104, 1116, 1180, 1198, 1222, 1312, 1446, 1558, 1642, 1686, 1780, 1794, 1804, 1900, 1902, 1974, 1996, 2038, 2040, 2076, 2286, 2392, 2428, 2448, 2458, 2460, 2478, 2518, 2584, 2596, 2602, 2668, 2736, 2742, 2788, 2800
Offset: 1

Views

Author

Artur Jasinski, Dec 13 2006

Keywords

Links

Crossrefs

Cf. A049407, similar sequences listed in A244376.

Programs

  • Magma
    [n: n in [0..3000]| IsPrime(1 + n + n^3 + n^5 + n^7+ n^9 + n^11 + n^13 )]; // Vincenzo Librandi, Nov 12 2010
  • Magma
    [n: n in [0..3000] | IsPrime(s) where s is 1+&+[n^i: i in [1..13 by 2]]]; // Vincenzo Librandi, Jun 28 2014
  • Mathematica
    Do[If[PrimeQ[1 + n + n^3 + n^5 + n^7 + n^9 + n^11 + n^13], Print[n]], {n, 1, 300}]
Select[Range[8000], PrimeQ[Total[#^Range[1, 13, 2]] + 1] &] (* Vincenzo Librandi, Jun 28 2014 *)
  • PARI
    is(n)=isprime(1+n+n^3+n^5+n^7+n^9+n^11+n^13) \\ Charles R Greathouse IV, Feb 20 2017

A124185 Numbers n such that 1 + n + n^3 + n^5 + n^7 + n^9 + n^11 + n^13 + n^15 + n^17 + n^19 + n^21 + n^23 + n^25 + n^27 is prime.

Original entry on oeis.org

182, 219, 393, 468, 629, 638, 755, 824, 960, 965, 984, 1002, 1053, 1068, 1095, 1110, 1140, 1209, 1233, 1269, 1457, 1518, 1539, 1547, 1590, 1622, 1659, 1707, 1797, 1818, 2174, 2259, 2333, 2799, 2975, 3032, 3074, 3272, 3285, 3338, 3368, 3477, 3564, 4118
Offset: 1

Views

Author

Artur Jasinski, Dec 13 2006

Keywords

Links

Crossrefs

Cf. A049407, similar sequences listed in A244376.

Programs

  • Magma
    [n: n in [0..5000] | IsPrime(s) where s is 1+&+[n^i: i in [1..27 by 2]]]; // Vincenzo Librandi, Jun 28 2014
  • Mathematica
    Do[If[PrimeQ[1 + n + n^3 + n^5 + n^7 + n^9 + n^11 + n^13 + n^15 + n^17 + n^19 + n^21 + n^23 + n^25 + n^27], Print[n]], {n, 1, 1400}]
Select[Range[5000], PrimeQ[Total[#^Range[1, 27, 2]] + 1] &] (* Vincenzo Librandi, Jun 28 2014 *)
  • PARI
    is(n)=isprime(1+n+n^3+n^5+n^7+n^9+n^11+n^13+n^15+n^17+n^19+n^21+n^23+n^25+n^27) \\ Charles R Greathouse IV, Feb 20 2017

A124200 Numbers n such that 1 + n + n^3 + n^5 + n^7 + n^9 + n^11 + n^13 + n^15 + n^17 + n^19 + n^21 + n^23 + n^25 + n^27 + n^29 + n^31 + n^33 + n^35 + n^37 + n^39 + n^41 + n^43 is prime.

Original entry on oeis.org

1, 7, 10, 171, 304, 322, 357, 385, 418, 436, 448, 592, 606, 628, 642, 858, 1065, 1186, 1438, 1543, 1639, 1843, 1848, 1879, 1899, 2110, 2241, 2517, 2544, 2578, 2668, 3195, 3207, 3306, 3307, 3657, 4137, 4177, 4329, 4617, 4837, 4945, 4956, 5026, 5281, 5509
Offset: 1

Views

Author

Artur Jasinski, Dec 13 2006

Keywords

Links

Crossrefs

Cf. A049407, similar sequences listed in A244376.

Programs

  • Magma
    [n: n in [0..5000] | IsPrime(s) where s is 1+&+[n^i: i in [1..43 by 2]]]; // Vincenzo Librandi, Jun 28 2014
  • Mathematica
    Do[If[PrimeQ[1 + n + n^3 + n^5 + n^7 + n^9 + n^11 + n^13 + n^15 + n^17 + n^19 + n^21 + n^23 + n^25 + n^27 + n^29 + n^31 + n^33 + n^35 + n^37 + n^39 + n^41 + n^43], Print[n]], {n, 1, 2400}]
Select[Range[6000], PrimeQ[Total[#^Range[1, 43, 2]] + 1] &] (* Vincenzo Librandi, Jun 28 2014 *)
  • PARI
    is(n)=isprime(1+n+n^3+n^5+n^7+n^9+n^11+n^13+n^15+n^17+n^19+n^21+n^23 + n^25+n^27+n^29+n^31+n^33+n^35+n^37+n^39+n^41+n^43) \\ Charles R Greathouse IV, Feb 20 2017

A124209 Numbers n such that 1 + n + n^3 + n^5 + n^7 + n^9 + n^11 + ... + n^61 + n^63 is prime.

Original entry on oeis.org

5, 15, 140, 359, 615, 876, 941, 1109, 1230, 1292, 1302, 1325, 1752, 1799, 2064, 2535, 2645, 2690, 2942, 3042, 3138, 3200, 3449, 3473, 3527, 3560, 3713, 4070, 4488, 4658, 4767, 5055, 5169, 5195, 5472, 5592, 5604, 5841, 5856, 5939, 6201, 6669, 6677, 6731, 6857
Offset: 1

Views

Author

Artur Jasinski, Dec 13 2006

Keywords

Links

Crossrefs

Cf. A049407, similar sequences listed in A244376.

Programs

  • Magma
    [n: n in [0..5000] | IsPrime(s) where s is 1+&+[n^i: i in [1..63 by 2]]]; // Vincenzo Librandi, Jun 28 2014
  • Maple
    a:= proc(n) option remember; local k;
      for k from 1+`if`(n=1, 1, a(n-1)) while
        not isprime(1+(k^65-k)/(k^2-1)) do od; k
    end:
seq(a(n), n=1..30);  # Alois P. Heinz, Jun 26 2014
  • Mathematica
    Do[If[PrimeQ[1 + n + n^3 + n^5 + n^7 + n^9 + n^11 + n^13 + n^15 + n^17 + n^19 + n^21 + n^23 + n^25 + n^27 + n^29 + n^31 + n^33 + n^35 + n^37 + n^39 + n^41 + n^43 + n^45 + n^47 + n^49 + n^51 + n^53 + n^55 + n^57 + n^59 + n^61 + n^63],Print[n]],{n,1,2400}]
Select[Range[7000], PrimeQ[Total[#^Range[1, 63, 2]] + 1] &] (* Vincenzo Librandi, Jun 28 2014 *)
  • PARI
    for(n=1,10^4,if(ispseudoprime(sum(i=0,31,n^(2*i+1))+1),print1(n,", "))) \\ Derek Orr, Jun 24 2014

Extensions

a(28) and beyond from Derek Orr, Jun 24 2014

A124150 Numbers n for which 1+n+n^3+n^5+n^7 is prime.

Original entry on oeis.org

1, 4, 15, 34, 39, 45, 55, 60, 103, 117, 123, 127, 129, 142, 172, 183, 190, 214, 222, 223, 234, 243, 265, 294, 337, 343, 354, 357, 472, 484, 495, 502, 510, 514, 520, 525, 552, 562, 600, 625, 628, 640, 652, 660, 663, 685, 748, 754, 775, 865, 885, 975, 979
Offset: 1

Views

Author

Artur Jasinski, Dec 13 2006

Keywords

Links

Crossrefs

Cf. similar sequences listed in A244376.

Programs

  • Magma
    [n: n in [0..900] | IsPrime(s) where s is 1+&+[n^i: i in [1..7 by 2]]]; // Vincenzo Librandi, Jun 27 2014
  • Mathematica
    Do[If[PrimeQ[1 + n + n^3 + n^5 + n^7], Print[n]], {n, 1, 1000}]
Select[Range[1000],PrimeQ[1+#+#^3+#^5+#^7]&] (* Harvey P. Dale, Jul 16 2013 *)
Select[Range[1000], PrimeQ[Total[#^Range[1, 7, 2]] + 1] &] (* Vincenzo Librandi, Jun 27 2014 *)

A124186 Numbers n such that 1 + n + n^3 + n^5 + n^7 + n^9 + n^11 + ... + n^27 + n^29 + n^31 is prime.

Original entry on oeis.org

1, 16, 25, 27, 93, 121, 187, 211, 267, 402, 420, 480, 601, 612, 631, 646, 667, 906, 916, 982, 1023, 1083, 1131, 1221, 1248, 1297, 1326, 1365, 1485, 1518, 1683, 1687, 1806, 1816, 1840, 1881, 1975, 1978, 2001, 2070, 2098, 2187, 2275, 2376, 2382, 2478, 2563, 2643, 2836, 3037, 3043
Offset: 1

Views

Author

Artur Jasinski, Dec 13 2006

Keywords

Comments

n can't be congruent to 2 mod 3, nor to 4 mod 5. - Robert Israel, Jun 24 2014

Links

Crossrefs

Cf. A049407, similar sequences listed in A244376.

Programs

  • Magma
    [n: n in [0..5000] | IsPrime(s) where s is 1+&+[n^i: i in [1..31 by 2]]]; // Vincenzo Librandi, Jun 28 2014
  • Maple
    filter:= n -> isprime(1+add(n^(2*k+1),k=0..15));
select(filter, [$1..10000]); # Robert Israel, Jun 24 2014
  • Mathematica
    Select[Range[100], PrimeQ[1 + Sum[#^(2k + 1), {k, 0, 15}]] &] (* Alonso del Arte, Jun 24 2014 *)
Select[Range[4000], PrimeQ[Total[#^Range[1, 31, 2]] + 1] &] (* Vincenzo Librandi, Jun 28 2014 *)
  • PARI
    for(n=1,10^4,if(ispseudoprime(sum(i=0,15,n^(2*i+1))+1),print1(n,", "))) \\ Derek Orr, Jun 24 2014
  • Sage
    i,n = var('i,n')
[n for n in (1..3100) if is_prime(1+(n^(2*i+1)).sum(i,0,15))] # Bruno Berselli, Jun 28 2014

Extensions

a(46)-a(51) from Derek Orr, Jun 24 2014
Showing 1-10 of 26 results. Next

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