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A023688
Numbers with exactly 6 ones in binary expansion.
19
63, 95, 111, 119, 123, 125, 126, 159, 175, 183, 187, 189, 190, 207, 215, 219, 221, 222, 231, 235, 237, 238, 243, 245, 246, 249, 250, 252, 287, 303, 311, 315, 317, 318, 335, 343, 347, 349, 350, 359, 363, 365, 366, 371, 373
OFFSET
1,1
COMMENTS
Sequence appears to include all numbers m such that 8^5 is the highest power of 2 dividingA005148(m). General conjecture: numbers k such that 8^j is the highest power of 2 dividingA005148(k) is the same sequence as numbers having exactly (j+1) 1's in their binary representation. -Benoit Cloitre,Jun 22 2002
LINKS
Robert Baillie,Summing the curious series of Kempner and Irwin,arXiv:0806.4410 [math.CA], 2008-2015. See p. 18 for Mathematica code irwinSums.m.
FORMULA
a(n+1) =A057168(a(n)). -M. F. Hasler,Aug 27 2014
Sum_{n>=1} 1/a(n) = 1.387753111935705074750004158584017188750706394077047633137401652680870607884... (calculated using Baillie's irwinSums.m, see Links). -Amiram Eldar,Feb 14 2022
MATHEMATICA
Select[ Range[ 63, 380 ], (Count[ IntegerDigits[ #, 2 ], 1 ]==6)& ]
PROG
(PARI) is_A023688(n)=hammingweight(n)==6 \\M. F. Hasler,Aug 27 2014
(PARI) print1(t=2^6-1); for(i=2, 50, print1( "," t=A057168(t))) \\M. F. Hasler,Aug 27 2014
KEYWORD
nonn,base,easy
STATUS
approved