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

1,1

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

Links

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

Example

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

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 *)

Prog

(PARI) isA077654(n) = !(isprime(n)) & !(isprime(2*n+1)); \\ Michael B. Porter, Oct 01 2009
(Magma) [n: n in [1..200] | not IsPrime(n) and not IsPrime(2*n+1)]; // Vincenzo Librandi, Apr 09 2015
(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

Crossrefs

Cf. A005384, A005385, A067812.

Sequence in context: A239055 A295129 A287338 * A095275 A366530 A117099

Adjacent sequences: A077651 A077652 A077653 * A077655 A077656 A077657

Keyword

nonn

Author

Lior Manor, Nov 13 2002

Extensions

Offset corrected by Eric M. Schmidt, Apr 09 2015

Status

approved