A123059 -id:A123059 - cp's OEIS frontend

A123076 Numbers k such that p = 1 + 2k + 3k^2 + 4k^3 is prime.

4, 12, 14, 18, 22, 24, 28, 34, 52, 62, 64, 78, 94, 104, 110, 118, 122, 132, 140, 144, 154, 158, 160, 178, 194, 204, 214, 218, 220, 234, 258, 262, 270, 272, 290, 294, 312, 314, 322, 344, 368, 370, 372, 382, 388, 424, 430, 440, 442, 454, 482, 494, 498, 518, 542

Offset: 1

Zak Seidov, Sep 27 2006

Corresponding p's are in A123059.

			For k=4, 1 + 2k + 3k^2 + 4k^3 = 313 which is prime.

James C. McMahon, Table of n, a(n) for n = 1..10000

Cf. A056578, A123059.

Select[Range[542],PrimeQ[1+2#+3#^2+4#^3]&] (* James C. McMahon, Nov 15 2024 *)

lista(m) = {for (n=1, m, if (isprime(1 + 2*n + 3*n^2 + 4*n^3), print1(n, ", ")););} \\ Michel Marcus, Apr 19 2013

A123077 Primes of the form (1+2n+3n^2+4n^3)/2.

Original entry on oeis.org

5, 71, 293, 7103, 32213, 40487, 50069, 87623, 161831, 211007, 238949, 337343, 852263, 922037, 1328447, 1421909, 1955399, 2607989, 3061703, 3744551, 4121087, 4318469, 4731941, 5400359, 5879231, 7198421, 9356927, 10400501, 10764863

Offset: 1

Zak Seidov, Sep 27 2006

Corresponding n's are 1, 3, 5, 15, 25, 27, 29, 35, 43, 47, 49, 55, 75, 77, 87, 89, 99, 109, 115, 123, 127, 129, 133, 139, 143, 153, 167, 173, 175, 179, 183, 185, 195, 199, 207, 209, 227, 229, 239, 245, 257, 259, 269, 273, 283, 285, 299, 309, 315, 325, 327, 337, 347, 349, 357, 363, 369, 377, 379, 393, 399, 403, 409, 417, 425, 439, 523, 539, 545, 559, 567, 575, 587, 589, 593, 607, 623, 659, 687, 697, 699.

There are no primes of the form (1+2n+3n^2+4n^3)/3.

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

Cf. A056578, A123059.

[a: n in [0..250] | IsPrime(a) where a is  (1 + 2*n + 3*n^2 + 4*n^3) div 2]; // Vincenzo Librandi, Mar 21 2013

Select[Table[(1 + 2 n + 3 n^2 + 4 n^3)/2, {n, 0, 200}], PrimeQ] (* Vincenzo Librandi, Mar 21 2013 *)

A123100 Primes of the form (1+2n+3n^2+4n^3)/5.

Original entry on oeis.org

2, 197, 354677, 713357, 959597, 1256837, 3676037, 5168717, 7018997, 11945957, 15099437, 18764117, 25303637, 36170597, 42610877, 46099517, 49773557, 71092757, 75979997, 91974917, 110070437, 123365117, 161190317, 306442277

Offset: 1

Zak Seidov, Sep 27 2006

All terms > 2 are congruent to 7 (mod 10).

Corresponding n's are: 1, 6, 76, 96, 106, 116, 166, 186, 206, 246, 266, 286, 316, 356, 376, 386, 396, 446, 456, 486, 516, 536, 586, 726, 736, 746, 766, 796, 846, 866, 906, 916, 1036, 1046, 1076, 1116, 1126, 1156, 1176, 1236, 1296, 1316, 1326, 1406, 1456, 1546, 1586, 1596, 1686, 1706, 1786, 1816, 1896, 1926, 1956, all are congruent to 1 (mod 5).

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

Cf. A056578, A123059.

Select[Table[(1 + 2 n + 3 n^2 + 4 n^3)/5, {n, 0, 200}], PrimeQ] (* Vincenzo Librandi, Mar 21 2013 *)

cp's OEIS Frontend

A123076 Numbers k such that p = 1 + 2k + 3k^2 + 4k^3 is prime.

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A123077 Primes of the form (1+2n+3n^2+4n^3)/2.

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A123100 Primes of the form (1+2n+3n^2+4n^3)/5.

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