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A014312
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Numbers with exactly 4 ones in binary expansion.
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20
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15, 23, 27, 29, 30, 39, 43, 45, 46, 51, 53, 54, 57, 58, 60, 71, 75, 77, 78, 83, 85, 86, 89, 90, 92, 99, 101, 102, 105, 106, 108, 113, 114, 116, 120, 135, 139, 141, 142, 147, 149, 150, 153, 154, 156, 163, 165, 166, 169, 170, 172, 177, 178, 180, 184, 195, 197
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graph;
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listen;
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internal format)
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OFFSET
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1,1
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LINKS
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FORMULA
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Sum_{n>=1} 1/a(n) = 1.399770961748474333075618147113153558623203796657745865012742162098738541849... (calculated using Baillie's irwinSums.m, see Links). - Amiram Eldar, Feb 14 2022
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MATHEMATICA
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Select[ Range[ 180 ], (Count[ IntegerDigits[ #, 2 ], 1 ]==4)& ] (* Olivier Gérard *)
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PROG
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(Perl) $N = 4;
my $vector = 2 ** $N - 1; # first key (15)
for (1..100) {
print "$vector, ";
my ($v, $d) = ($vector, 0);
until ($v & 1 or !$v) { $d = ($d << 1)|1; $v >>= 1 }
$vector += $d + 1 + (($v ^ ($v + 1)) >> 2); # next key
(PARI) for(n=0, 10^3, if(hammingweight(n)==4, print1(n, ", "))); \\ Joerg Arndt, Mar 04 2014
(Python)
A014312_list = [2**a+2**b+2**c+2**d for a in range(3, 6) for b in range(2, a) for c in range(1, b) for d in range(c)] # Chai Wah Wu, Jan 24 2021
(Rust)
pub const fn next_choice(value: usize) -> usize {
// Passing a term will return the next number in the sequence
let zeros = value.trailing_zeros();
let ones = (value >> zeros).trailing_ones();
value + (1 << zeros) + (1 << (ones - 1)) - 1
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CROSSREFS
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Cf. A000079, A018900, A014311, A014313, A023688, A023689, A023690, A023691 (Hamming weight = 1, 2, ..., 9), A057168.
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KEYWORD
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nonn,base,easy
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AUTHOR
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Al Black (gblack(AT)nol.net)
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EXTENSIONS
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STATUS
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approved
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