A173589 Integers whose binary representation contains exactly three 1's, no two 1's being adjacent.

21, 37, 41, 42, 69, 73, 74, 81, 82, 84, 133, 137, 138, 145, 146, 148, 161, 162, 164, 168, 261, 265, 266, 273, 274, 276, 289, 290, 292, 296, 321, 322, 324, 328, 336, 517, 521, 522, 529, 530, 532, 545, 546, 548, 552, 577, 578, 580, 584, 592, 641, 642, 644, 648

Offset: 1

Author

David Koslicki (koslicki(AT)math.psu.edu), Feb 22 2010

Keywords

• base
• nonn

Comments

Subsequence of A014311. [R. J. Mathar, Feb 24 2010]

A000120(a(n))=3; A023416(a(n))>1; 1 < A087116(a(n))<=3. [Reinhard Zumkeller, Mar 11 2010]

Examples

			a(1) = 21 = 10101_2.
a(2) = 37 = 100101_2.
a(3) = 41 = 101001_2.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000120, A014311, A023416, A087116.

Programs

Maple

seq(seq(seq(2^a+2^b+2^c, c=0..b-2),b=2..a-2),a=4..10); # Robert Israel, Dec 19 2016

Mathematica

e31sQ[n_]:=Module[{idn2=IntegerDigits[n,2]},Total[idn2]==3 && SequenceCount[ idn2,{1,1}]==0]; Select[Range[700],e31sQ] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Sep 20 2018 *)

Python

from math import isqrt, comb
from sympy import integer_nthroot
def A173589(n): return (1<<(r:=n-1-comb((m:=integer_nthroot(6*n,3)[0])+(t:=(n>comb(m+2,3)))+1,3))-comb((k:=isqrt(b:=r+1<<1))+(b>k*(k+1)),2))+(1<<(a:=isqrt(s:=n-comb(m-(t^1)+2,3)<<1))+((s<<2)>(a<<2)*(a+1)+1)+1)+(1<Chai Wah Wu, Apr 07 2025

Extensions

More terms from R. J. Mathar, Feb 24 2010