A269264 -id:A269264 - cp's OEIS frontend

A360993 Numbers k such that (2^k - 1)^3 + 2 is a semiprime.

4, 5, 8, 12, 13, 18, 20, 29, 38, 56, 60, 62, 76, 82, 101, 118, 202, 210, 230, 276, 328, 332, 336, 338, 368

Offset: 1

Serge Batalov, Feb 27 2023

a(26) >= 406.
438, 500, 526, 604, 648, 696 are also in this sequence, but their positions cannot be established before finding any factor for the values corresponding to the following "blockers": 406, 496, 528.
2382, 2733, 2910, 3368, 3508, 5338, 7705, 11185, 19905, 23814, 38545, 179294 are larger terms of this sequence, but their positions cannot be established. These produce "trivial" semiprimes where one prime is small (e.g., 3 or 11).

			a(1) = 4 because 15^3 + 2 = 3377 = 11 * 307, which is semiprime.
a(2) = 5 because 31^3 + 2 = 29793 = 3 * 9931, which is semiprime.

factordb.com, Status of (2^406-1)^3+2.

Cf. A091515, A091516, A100899, A100900, A268574, A269264, A360994.

IsSemiprime:=func; [n: n in [2..70]| IsSemiprime(s) where s is (2^n-1)^3+2];

Mathematica

Select[Range[70], PrimeOmega[(2^# - 1)^3 - 2] == 2 &]

PARI

isok(n) = bigomega((2^n-1)^3+2) == 2;

Extensions

a(20)-a(26) from Serge Batalov, Mar 03 2023

A360994 Numbers k such that (2^k + 1)^3 - 2 is a semiprime.

Original entry on oeis.org

0, 1, 2, 4, 5, 6, 13, 14, 18, 27, 43, 45, 63, 76, 85, 108, 115, 119, 123, 187, 211, 215, 283, 312

Offset: 1

Serge Batalov, Feb 27 2023

a(25) >= 355.
623, 674, 711, 766, 767 are also in this sequence, but their position cannot be established before finding any factor for the values corresponding to the following "blockers": 355, 511, 587, 707, 731.
1424, 1470, 1580, 1946, 2117, 2693, 3000, 3540, 4164, 7043, 9475, 10632, 15018, 19064, 27130, 28266, 28532, 46434, 58768, 103536 are some larger members of this sequence, but their position cannot be established. These produce "trivial" semiprimes where one prime is small (e.g., 3 or 5).

factordb.com, Status of (2^355+1)^3-2.

Cf. A001358, A091513, A091514, A093069, A099359, A100899, A100900, A269264, A360993.

IsSemiprime:=func; [n: n in [1..70]| IsSemiprime(s) where s is (2^n+1)^3-2];

Mathematica

Select[Range[70], PrimeOmega[(2^# + 1)^3 - 2] == 2 &]

PARI

isok(n) = bigomega((2^n+1)^3-2) == 2;

Formula

{ k >= 0 : A099359(k) in { A001358 } }.

A268574 Numbers k such that (2^k + 1)^2 - 2 is a semiprime.

Original entry on oeis.org

4, 6, 7, 10, 11, 14, 22, 36, 38, 39, 44, 45, 48, 49, 60, 72, 74, 75, 89, 92, 96, 99, 105, 110, 111, 113, 116, 131, 138, 143, 150, 170, 173, 182, 194, 201, 212, 234, 260, 282, 300, 317, 335, 341, 345, 383, 405

Offset: 1

Vincenzo Librandi, Feb 21 2016

a(48) >= 428. - Serge Batalov, Feb 25 2023

			a(1) = 4 because 17^2 - 2 = 287 = 7*41, which is semiprime.
a(2) = 6 because 65^2 - 2 = 4223 = 41*103, which is semiprime.

factordb.com, Status of (2^428+1)^2-2.

Cf. A091513, A091514, A093069, A269264, A360993, A360994.

IsSemiprime:=func; [n: n in [1..110]| IsSemiprime(s) where s is (2^n+1)^2-2];

Mathematica

Select[Range[105], PrimeOmega[(2^# + 1)^2 - 2] == 2 &]

PARI

isok(n) = bigomega((2^n+1)^2-2) == 2; \\ Michel Marcus, Feb 22 2016

Extensions

a(25)-a(39) from Hugo Pfoertner, Aug 05 2019

a(40)-a(41) from chris2be8@yahoo.com, Feb 25 2023

a(42)-a(47) from Serge Batalov, Feb 26 2023

cp's OEIS Frontend

A360993 Numbers k such that (2^k - 1)^3 + 2 is a semiprime.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Magma

Mathematica

PARI

Extensions

A360994 Numbers k such that (2^k + 1)^3 - 2 is a semiprime.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Magma

Mathematica

PARI

Formula

A268574 Numbers k such that (2^k + 1)^2 - 2 is a semiprime.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Magma

Mathematica

PARI

Extensions