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A014312 Numbers with exactly 4 ones in binary expansion. 16
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 (list; graph; refs; listen; history; text; internal format)
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]

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

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

CROSSREFS

Cf. A090706.

Cf. A000079, A018900, A014311, A014312, A014313, A023688, A023689, A023690, A023691 (Hamming weight = 1, 2, ..., 9), A057168.

Cf. A194882, A194883, A194884, A127324.

Sequence in context: A219683 A166665 A317295 * A325823 A129387 A341170

Adjacent sequences:  A014309 A014310 A014311 * A014313 A014314 A014315

KEYWORD

nonn,base,easy

AUTHOR

Al Black (gblack(AT)nol.net)

EXTENSIONS

Extension by Olivier Gérard

STATUS

approved

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Last modified April 15 20:40 EDT 2021. Contains 342977 sequences. (Running on oeis4.)