A077654 Composites k such that 2k+1 is also composite.

4, 10, 12, 16, 22, 24, 25, 27, 28, 32, 34, 38, 40, 42, 45, 46, 49, 52, 55, 57, 58, 60, 62, 64, 66, 70, 72, 76, 77, 80, 82, 84, 85, 87, 88, 91, 92, 93, 94, 100, 102, 104, 106, 108, 110, 112, 115, 117, 118, 121, 122, 123, 124, 126, 129, 130, 132, 133, 136, 142

Offset: 1

Author

Lior Manor, Nov 13 2002

Keywords

• nonn

Comments

Sequence is infinite. For instance, it contains 2^m for m not of the form 2^k - 1. - Eric M. Schmidt, Apr 09 2015

Examples

			Both 16 and 33 = 16*2 + 1 are composite, so 16 is in this sequence.
		

Links

• Eric M. Schmidt, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A005384, A005385, A067812.

Programs

Magma

[n: n in [1..200] | not IsPrime(n) and not IsPrime(2*n+1)]; // Vincenzo Librandi, Apr 09 2015

Mathematica

Select[Range[200], !PrimeQ[#] && !PrimeQ[2 # + 1] &] (* Vincenzo Librandi, Apr 09 2015 *)
Select[Range[200],AllTrue[{#,2#+1},CompositeQ]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jun 12 2019 *)

PARI

isA077654(n) = !(isprime(n)) & !(isprime(2*n+1)); \\ Michael B. Porter, Oct 01 2009

Python

from sympy import isprime
def ok(n): return n >= 4 and not isprime(2*n+1) and not isprime(n)
print(list(filter(ok, range(4, 143)))) # Michael S. Branicky, Apr 10 2021

Extensions

Offset corrected by Eric M. Schmidt, Apr 09 2015