A086097 - OEIS

%I #14 Dec 03 2021 12:59:35

%S 57,85,141,177,201,393,537,553,633,697,717,745,921,933,1141,1285,1345,

%T 1477,1641,1713,1761,1981,1982,2041,2181,2361,2433,2558,2577,2605,

%U 2761,2941,2977,3062,3117,3241,3273,3326,3397,3578,3721,3777,3901,3902,3957

%N Numbers n such that n and n+1 are semiprimes with a semiprime number of 1's in their binary representation.

%C 3721 is the first square entry. Conjecture: sequence is infinite.

%H Amiram Eldar, <a href="/A086097/b086097.txt">Table of n, a(n) for n = 1..10000</a>

%t binWt[n_] := DigitCount[n, 2, 1]; seqQ[n_] := PrimeOmega[n] == 2 && PrimeOmega[binWt[n]] == 2; Select[Range[4000], seqQ[#] && seqQ[#+1] &] (* _Amiram Eldar_, Dec 14 2019 *)

%t SequencePosition[Table[If[PrimeOmega[n]==PrimeOmega[DigitCount[n,2,1]]==2,1,0],{n,4000}],{1,1}][[All,1]] (* _Harvey P. Dale_, Dec 03 2021 *)

%o (PARI) issemi(n)=bigomega(n)==2

%o is(n)=issemi(hammingweight(n))&&issemi(hammingweight(n+1))&&issemi(n)&&issemi(n+1) \\ _Charles R Greathouse IV_, Mar 28 2013

%Y Subsequence of A070552 and of A086096.

%Y Cf. A001358, A000120.

%K nonn,base

%O 1,1

%A _Jason Earls_, Jul 09 2003