login
A014312
Numbers with exactly 4 ones in binary expansion.
20
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
OFFSET
1,1
LINKS
T. D. Noe and Ivan Neretin, Table of n, a(n) for n = 1..10000 (terms 1..1000 from T. D. Noe)
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
a(n) = 2^A194882(n-1) + 2^A194883(n-1) + 2^A194884(n-1) + 2^A127324(n-1). - Ridouane Oudra, Sep 06 2020
Sum_{n>=1} 1/a(n) = 1.399770961748474333075618147113153558623203796657745865012742162098738541849... (calculated using Baillie's irwinSums.m, see Links). - Amiram Eldar, Feb 14 2022
MATHEMATICA
Select[ Range[ 180 ], (Count[ IntegerDigits[ #, 2 ], 1 ]==4)& ] (* Olivier Gérard *)
PROG
(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
} # Ruud H.G. van Tol, Mar 02 2014
(PARI) for(n=0, 10^3, if(hammingweight(n)==4, print1(n, ", "))); \\ Joerg Arndt, Mar 04 2014
(PARI) print1(t=15); for(i=2, 50, print1(", "t=A057168(t))) \\ M. F. Hasler, Aug 27 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
} // Andrew Bennett, Jan 07 2022
CROSSREFS
Cf. A090706.
Cf. A000079, A018900, A014311, A014313, A023688, A023689, A023690, A023691 (Hamming weight = 1, 2, ..., 9), A057168.
Sequence in context: A219683 A166665 A317295 * A371894 A325823 A129387
KEYWORD
nonn,base,easy
AUTHOR
Al Black (gblack(AT)nol.net)
EXTENSIONS
Extension by Olivier Gérard
STATUS
approved