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A014311 Numbers with exactly 3 ones in binary expansion. 26
7, 11, 13, 14, 19, 21, 22, 25, 26, 28, 35, 37, 38, 41, 42, 44, 49, 50, 52, 56, 67, 69, 70, 73, 74, 76, 81, 82, 84, 88, 97, 98, 100, 104, 112, 131, 133, 134, 137, 138, 140, 145, 146, 148, 152, 161, 162, 164, 168, 176, 193, 194, 196, 200, 208, 224, 259, 261, 262, 265, 266, 268, 273, 274, 276, 280, 289, 290, 292, 296, 304 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Equivalently, sums of three distinct powers of 2.

Appears to give all n such that 64 is the highest power of 2 dividing A005148(n). - Benoit Cloitre, Jun 22 2002

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Stephen Morley, HAKMEM Item 175 (Gosper).

Tilman Piesk, First 56 elements in a tetrahedral array.

FORMULA

A000120(a(n)) = 3. [Reinhard Zumkeller, May 03 2012]

Start with A084468. If n is in sequence, then 2n is too. - Ralf Stephan, Aug 16 2013

a(n+1) = A057168(a(n)). - M. F. Hasler, Aug 27 2014

MATHEMATICA

Select[Range[200], (Count[IntegerDigits[#, 2], 1] == 3)&]

nn = 8; Flatten[Table[2^i + 2^j + 2^k, {i, 2, nn}, {j, 1, i - 1}, {k, 0, j - 1}]] (* T. D. Noe, Nov 05 2013 *)

PROG

(Haskell)

a014311 n = a014311_list !! (n-1)

a014311_list = [2^x + 2^y + 2^z |

                x <- [2..], y <- [1..x-1], z <- [0..y-1]]

-- Reinhard Zumkeller, May 03 2012

(C)

unsigned hakmem175(unsigned x) {

    unsigned s, o, r;

    s = x & -x;  r = x + s;

    o = r ^ x;  o = (o >> 2) / s;

    return r | o;

}

unsigned A014311(int n) {

    if (n == 1) return 7;

    return hakmem175(A014311(n - 1));

}  // Peter Luschny, Jan 01 2014

(PARI) for(n=0, 10^3, if(hammingweight(n)==3, print1(n, ", "))); \\ Joerg Arndt, Mar 04 2014

(PARI) print1(t=7); for(i=2, 50, print1(", "t=A057168(t))) \\ M. F. Hasler, Aug 27 2014

CROSSREFS

Cf. A038465 (base 3), A038471 (base 4), A038475 (base 5).

Cf. A081091 (primes), A212190 (squares), A212192 (triangular numbers).

Cf. A057168.

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

Sequence in context: A271499 A235336 A075930 * A245178 A287161 A051266

Adjacent sequences:  A014308 A014309 A014310 * A014312 A014313 A014314

KEYWORD

nonn,base,easy

AUTHOR

Al Black (gblack(AT)nol.net)

EXTENSIONS

Extension and program by Olivier Gérard

STATUS

approved

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Last modified June 25 22:15 EDT 2017. Contains 288730 sequences.