A099359 -id:A099359 - cp's OEIS frontend

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

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 } }.

A100496 Numbers n such that (2^n+1)^4-2 is prime.

Original entry on oeis.org

1, 7, 25, 31, 34, 271, 514, 2896, 8827, 16816, 37933

Offset: 1

Jonathan Vos Post, Nov 23 2004

Some of the results were computed using the PrimeFormGW (PFGW) primality-testing program. - Hugo Pfoertner, Nov 14 2019

a(12) > 60000. - Tyler Busby, Feb 12 2023

			a(1) = 1 because (2^1+1)^4 - 2 = 79 is prime and is the first such prime.

Cf. A091513, A091514, A093069, A099359.

Cf. A100497, n such that (2^n+1)^4-2 is semiprime.

Select[Range[5000], PrimeQ[(2^# + 1)^4 - 2] &]

is(n)=ispseudoprime((2^n+1)^4-2) \\ Charles R Greathouse IV, Jun 13 2017

Edited, corrected and extended by Ray Chandler and Hugo Pfoertner, Nov 26 2004

a(10)-a(11) from Tyler Busby, Feb 12 2023

A100900 Numbers n such that (2^n+1)^3-2 is prime.

Original entry on oeis.org

3, 7, 11, 15, 35, 16475, 26827, 79127, 85075

Offset: 1

Ray Chandler, Nov 21 2004

Next term > 88000.

471043 is in the sequence, but its position is not determined yet. - Serge Batalov, Jun 18 2016

S. Harvey, Carol and Kynea Primes.

Cf. A099359.

is(n)=(n%4==3 && ispseudoprime((2^n+1)^3-2)) \\ Charles R Greathouse IV, Feb 19 2016

cp's OEIS Frontend

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

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A100496 Numbers n such that (2^n+1)^4-2 is prime.

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A100900 Numbers n such that (2^n+1)^3-2 is prime.

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