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A077654
Composites k such that 2k+1 is also composite.
8
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
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
KEYWORD
nonn
AUTHOR
Lior Manor, Nov 13 2002
EXTENSIONS
Offset corrected by Eric M. Schmidt, Apr 09 2015
STATUS
approved