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A177221
Numbers k that are the products of two distinct primes such that 2*k + 1 is also the product of two distinct primes.
3
10, 34, 38, 46, 55, 57, 77, 91, 93, 106, 118, 123, 129, 133, 143, 145, 159, 161, 177, 185, 201, 203, 205, 206, 213, 218, 226, 235, 259, 267, 291, 295, 298, 305, 314, 327, 334, 335, 339, 358, 365, 377, 381, 394, 395, 403, 407, 415, 417, 446, 447, 458, 466, 469
OFFSET
1,1
LINKS
EXAMPLE
10 is in the sequence because 10 = 2*5 and 2*10+1 = 21 = 3*7.
MAPLE
isA006881:= proc(n) local F;
F:= ifactors(n)[2];
nops(F)=2 and F[1, 2]+F[2, 2]=2
end proc:
filter:= n -> andmap(isA006881, [n, 2*n+1]); select(filter, [$1..1000]); # Robert Israel, Nov 09 2017
MATHEMATICA
f[n_]:=Last/@FactorInteger[n]=={1, 1}; lst={}; Do[If[f[n]&&f[2*n+1], AppendTo[lst, n]], {n, 0, 3*6!}]; lst
Select[Range[500], PrimeNu[#]==PrimeOmega[#]==PrimeNu[2#+1] == PrimeOmega[ 2#+1] == 2&] (* Harvey P. Dale, Feb 22 2018 *)
KEYWORD
nonn
AUTHOR
STATUS
approved