A123608 Numbers k such that k, k+1 and 2*k+1 are composite.

24, 25, 27, 32, 34, 38, 45, 49, 55, 57, 62, 64, 76, 77, 80, 84, 85, 87, 91, 92, 93, 94, 104, 110, 115, 117, 118, 121, 122, 123, 124, 129, 132, 133, 142, 143, 144, 145, 147, 152, 154, 159, 160, 161, 164, 169, 170, 171, 175, 177, 182, 184, 185, 187, 188, 195, 201

Offset: 1

Author

Alexander Adamchuk, Nov 15 2006

Keywords

• nonn

Comments

Also numbers n such that A098735(n) = 1. Also numbers n such that A098077(n) divides n!. Note that n, n+1 and 2n+1 are all primes only for n = 2.

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A098735, A098077.

Programs

Mathematica

Select[Range[500],!PrimeQ[ # ]&&!PrimeQ[ #+1]&&!PrimeQ[2#+1]&]
Select[Range[250],AllTrue[{#,#+1,2#+1},CompositeQ]&] (* Harvey P. Dale, Jun 02 2025 *)