A049407 -id:A049407 - cp's OEIS frontend

A095692 Primes of the form n^3 + n + 1.

3, 11, 31, 131, 223, 521, 739, 1741, 3391, 4931, 5851, 9283, 24419, 27031, 32801, 59359, 68963, 74131, 85229, 110641, 148931, 157519, 175673, 216061, 328579, 357983, 405299, 456611, 571871, 658591, 857471, 1061311, 1124969, 1259821

Offset: 1

Giovanni Teofilatto, Jul 06 2004

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. A049407 (corresponding n).

[a: n in [0..200] | IsPrime(a) where a is n^3+n+1]; // Vincenzo Librandi, Jul 17 2012

f[n_]:=n^3+n+1; lst={};Do[If[PrimeQ[f[n]],AppendTo[lst,f[n]]],{n,5!}];lst (* Vladimir Joseph Stephan Orlovsky, Jul 27 2009 *)
Select[Table[n^3+n+1,{n,0,800}],PrimeQ] (* Vincenzo Librandi, Jul 17 2012 *)

Edited by Rick L. Shepherd, Jul 07 2004

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

Artur Jasinski, Dec 13 2006

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

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. A049407, similar sequences listed in A244376.

[n: n in [0..600] | IsPrime(s) where s is 1+&+[n^i: i in [1..5 by 2]]]; // Vincenzo Librandi, Jun 27 2014

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 *)

forstep(n=2,1000,2,if(isprime(1 + n + n^3 + n^5), print1(n","))) \\ Franklin T. Adams-Watters, Apr 09 2009

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

Artur Jasinski, Dec 13 2006

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. A049407, similar sequences listed in A244376.

[n: n in [0..1500]| IsPrime(1 + n + n^3 + n^5 + n^7+ n^9 )]; // Vincenzo Librandi, Nov 13 2010

[n: n in [0..1200] | IsPrime(s) where s is 1+&+[n^i: i in [1..9 by 2]]]; // Vincenzo Librandi, Jun 27 2014

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 *)

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

Artur Jasinski, Dec 13 2006

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. A049407, similar sequences listed in A244376.

[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

[n: n in [0..3000] | IsPrime(s) where s is 1+&+[n^i: i in [1..13 by 2]]]; // Vincenzo Librandi, Jun 28 2014

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 *)

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

Artur Jasinski, Dec 13 2006

Vincenzo Librandi, Table of n, a(n) for n = 1..850

Cf. A049407, similar sequences listed in A244376.

[n: n in [0..5000] | IsPrime(s) where s is 1+&+[n^i: i in [1..27 by 2]]]; // Vincenzo Librandi, Jun 28 2014

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 *)

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

A124187 Numbers n such that 1 + n + n^3 + n^5 + n^7 + n^9 + n^11 + ... + n^33 + n^35 is prime.

Original entry on oeis.org

1, 7, 10, 17, 52, 69, 108, 161, 173, 231, 306, 330, 338, 352, 416, 582, 584, 593, 635, 767, 834, 855, 868, 892, 927, 944, 950, 1044, 1060, 1203, 1242, 1299, 1302, 1509, 1520, 1551, 1637, 1972, 2067, 2078, 2135, 2303, 2310, 2366, 2416, 2511, 2514, 2556, 2581

Offset: 1

Artur Jasinski, Dec 13 2006

nonn

Vincenzo Librandi, Table of n, a(n) for n = 1..258

Cf. A049407.

[n: n in [0..4000] | IsPrime(1+n*(1+n^2)*(1+n^4+n^8)*(1+n^12+n^24))]; // Vincenzo Librandi, Jun 27 2014

a:= proc(n) option remember; local k;
      for k from 1+ a(n-1) while
        not isprime(1+(k^37-k)/(k^2-1)) do od; k
    end: a(1):=1:
seq(a(n), n=1..30);  # Alois P. Heinz, Jun 26 2014

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],Print[n]],{n,1,2400}]
Select[Range[5000], PrimeQ[Total[#^Range[1, 35, 2]] + 1] &] (* Vincenzo Librandi, Jun 27 2014 *)

for(n=1,10^4,if(ispseudoprime(sum(i=0,17,n^(2*i+1))+1),print1(n,", "))) \\ Derek Orr, Jun 24 2014

a(45) and beyond from Derek Orr, Jun 24 2014

A124189 Numbers n such that 1 + n + n^3 + n^5 + n^7 + n^9 + n^11 + ... + n^37 + n^39 is prime.

Original entry on oeis.org

42, 47, 60, 119, 153, 179, 195, 236, 269, 287, 383, 821, 846, 921, 924, 1104, 1181, 1200, 1349, 1806, 1917, 1980, 2015, 2049, 2057, 2369, 2394, 2522, 2660, 2876, 2882, 2940, 2991, 3206, 3311, 3570, 3695, 3741, 3785, 3840, 3944, 3966, 4049, 4148, 4377, 4448

Offset: 1

Artur Jasinski, Dec 13 2006

nonn

Vincenzo Librandi, Table of n, a(n) for n = 1..195

Cf. A049407.

[n: n in [0..4000] | IsPrime(s) where s is 1+&+[n^i: i in [1..39 by 2]]]; // Vincenzo Librandi, Nov 12 2010, revised Jun 27 2014

a:= proc(n) option remember; local k;
      for k from 1 +`if`(n=1, 1, a(n-1)) while
        not isprime(1+(k^41-k)/(k^2-1)) do od; k
    end:
seq(a(n), n=1..40);  # Alois P. Heinz, Jun 26 2014

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],Print[n]],{n,1,2400}]
Select[Range[5000], PrimeQ[Total[#^Range[1, 39, 2]] + 1] &] (* Vincenzo Librandi, Jun 27 2014 *)

for(n=1, 10^4, if(ispseudoprime(sum(i=0, 19, n^(2*i+1))+1), print1(n,", "))) \\ Derek Orr, Jun 24 2014

a(43) and beyond from Derek Orr, Jun 24 2014

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

Artur Jasinski, Dec 13 2006

Vincenzo Librandi, Table of n, a(n) for n = 1..620

Cf. A049407, similar sequences listed in A244376.

[n: n in [0..5000] | IsPrime(s) where s is 1+&+[n^i: i in [1..43 by 2]]]; // Vincenzo Librandi, Jun 28 2014

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 *)

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

A124205 Numbers n such that 1 + n + n^3 + n^5 + n^7 + n^9 + n^11 + ... + n^45 + n^47 is prime.

Original entry on oeis.org

12, 18, 39, 75, 82, 92, 133, 152, 273, 428, 568, 617, 749, 922, 949, 975, 1020, 1033, 1058, 1088, 1113, 1207, 1253, 1329, 1372, 1389, 1762, 1784, 1882, 1943, 1950, 1962, 1969, 2372, 2445, 2508, 2594, 2768, 2973, 2977, 3237, 3327, 3338, 3459, 3545, 3550, 3554

Offset: 1

Artur Jasinski, Dec 13 2006

nonn

Vincenzo Librandi, Table of n, a(n) for n = 1..362

Cf. A049407.

[n: n in [0..4000] | IsPrime(s) where s is 1+&+[n^i: i in [1..47 by 2]]]; // Vincenzo Librandi, Jun 27 2014, after Derek Orr

a:= proc(n) option remember; local k;
      for k from 1+`if`(n=1, 1, a(n-1)) while
        not isprime(1+(k^49-k)/(k^2-1)) do od; k
    end:
seq(a(n), n=1..40);  # Alois P. Heinz, Jun 26 2014

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], Print[n]], {n, 1, 2400}] (* Artur Jasinski *)
Select[Range[2500], PrimeQ[Total[#^Range[1, 47, 2]] + 1] &] (* Harvey P. Dale, Jan 13 2011 *)

for(n=1,10^4,if(ispseudoprime(sum(i=0,23,n^(2*i+1))+1),print1(n,", "))) \\ Derek Orr, Jun 24 2014

a(35) and beyond from Derek Orr, Jun 24 2014

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

Artur Jasinski, Dec 13 2006

Chai Wah Wu, Table of n, a(n) for n = 1..1237 (n = 1..230 from Vincenzo Librandi)

Cf. A049407, similar sequences listed in A244376.

[n: n in [0..5000] | IsPrime(s) where s is 1+&+[n^i: i in [1..63 by 2]]]; // Vincenzo Librandi, Jun 28 2014

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

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 *)

for(n=1,10^4,if(ispseudoprime(sum(i=0,31,n^(2*i+1))+1),print1(n,", "))) \\ Derek Orr, Jun 24 2014

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

cp's OEIS Frontend

A095692 Primes of the form n^3 + n + 1.

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

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

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

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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.

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A124187 Numbers n such that 1 + n + n^3 + n^5 + n^7 + n^9 + n^11 + ... + n^33 + n^35 is prime.

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A124189 Numbers n such that 1 + n + n^3 + n^5 + n^7 + n^9 + n^11 + ... + n^37 + n^39 is prime.

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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.