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A086097 Numbers n such that n and n+1 are semiprimes with a semiprime number of 1's in their binary representation. 2
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified June 26 21:14 EDT 2022. Contains 354885 sequences. (Running on oeis4.)