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A023688
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Numbers with exactly 6 ones in binary expansion.
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17
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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
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OFFSET
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1,1
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COMMENTS
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Sequence appears to include all numbers m such that 8^5 is the highest power of 2 dividing A005148(m). General conjecture: numbers k such that 8^j is the highest power of 2 dividing A005148(k) is the same sequence as numbers having exactly (j+1) 1's in their binary representation. - Benoit Cloitre, Jun 22 2002
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LINKS
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Ivan Neretin, Table of n, a(n) for n = 1..10000
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.
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FORMULA
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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
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MATHEMATICA
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Select[ Range[ 63, 380 ], (Count[ IntegerDigits[ #, 2 ], 1 ]==6)& ]
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PROG
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(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
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CROSSREFS
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Cf. A000079, A018900, A014311, A014312, A014313, A023689, A023690, A023691 (Hamming weight = 1..9).
Cf. A005148, A057168.
Sequence in context: A343003 A253021 A039480 * A118157 A257897 A261108
Adjacent sequences: A023685 A023686 A023687 * A023689 A023690 A023691
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KEYWORD
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nonn,base,easy
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AUTHOR
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Olivier Gérard
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STATUS
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approved
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