A086097 Numbers n such that n and n+1 are semiprimes with a semiprime number of 1's in their binary representation.

57, 85, 141, 177, 201, 393, 537, 553, 633, 697, 717, 745, 921, 933, 1141, 1285, 1345, 1477, 1641, 1713, 1761, 1981, 1982, 2041, 2181, 2361, 2433, 2558, 2577, 2605, 2761, 2941, 2977, 3062, 3117, 3241, 3273, 3326, 3397, 3578, 3721, 3777, 3901, 3902, 3957

Offset: 1

Author

Jason Earls, Jul 09 2003

Keywords

• nonn
• base

Comments

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

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Subsequence of A070552 and of A086096.

Cf. A001358, A000120.

Programs

Mathematica

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 *)
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 *)

PARI

issemi(n)=bigomega(n)==2
is(n)=issemi(hammingweight(n))&&issemi(hammingweight(n+1))&&issemi(n)&&issemi(n+1) \\ Charles R Greathouse IV, Mar 28 2013