OFFSET
1,1
COMMENTS
Numbers n such that both n and 2n+1 are in A111153.
If 29+30*k, 39+40*k and 47+48*k are all primes then 58+60*k is in the sequence. Thus Dickson's conjecture implies this sequence is infinite. - Robert Israel, Mar 17 2019
LINKS
Robert Israel, Table of n, a(n) for n = 1..10000
FORMULA
n, n1=2n+1 and n2=2n1+1 are semiprimes.
EXAMPLE
38=2*19, 2*38+1=77=7*11 and 2*77+1=155=5*31;
129=3*43, 2*129+1=259=7*37 and 2*259+1=519=3*173.
MAPLE
filter:= n -> andmap(numtheory:-bigomega=2, [n, 2*n+1, 4*n+3]):
select(filter, [$1..2000]); # Robert Israel, Mar 17 2019
MATHEMATICA
fQ[n_]:=2==Plus@@Last/@FactorInteger[n]; Select[Range[2000], fQ[ # ]&&fQ[2#+1]&&fQ[4#+3]&]
CROSSREFS
KEYWORD
nonn
AUTHOR
Zak Seidov, Sep 19 2007
STATUS
approved