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

1,1

Comments

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

Links

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

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 *)

Prog

(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

Crossrefs

Subsequence of A070552 and of A086096.

Cf. A001358, A000120.

Sequence in context: A087922 A087921 A196580 * A172333 A200932 A145554

Adjacent sequences: A086094 A086095 A086096 * A086098 A086099 A086100

Keyword

nonn,base

Author

Jason Earls, Jul 09 2003

Status

approved