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A057168 Next larger integer with same binary weight (number of 1 bits) as n. 16
2, 4, 5, 8, 6, 9, 11, 16, 10, 12, 13, 17, 14, 19, 23, 32, 18, 20, 21, 24, 22, 25, 27, 33, 26, 28, 29, 35, 30, 39, 47, 64, 34, 36, 37, 40, 38, 41, 43, 48, 42, 44, 45, 49, 46, 51, 55, 65, 50, 52, 53, 56, 54, 57, 59, 67, 58, 60, 61, 71, 62, 79, 95, 128, 66, 68, 69, 72, 70, 73, 75 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Binary weight is given by A000120.

REFERENCES

Beeler, M., Gosper, R. W. and Schroeppel, R. HAKMEM. MIT AI Memo 239, Feb 29 1972 (Item 175).

Donald Knuth, The Art of Computer Programming, Vol. 4A, section 7.1.3, exercises 20-21.

LINKS

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

Beeler, M., Gosper, R. W. and Schroeppel, R., HAKMEM ITEM 175

FORMULA

a(A000079(n))=A000079(n+1); a(A000051(n))=A052548(n); a(A052548(n))=A140504(n); a(A000225(n))=A055010(n); (A007283(n))=A000051(n+2). - Reinhard Zumkeller, Aug 18 2008

a(n) = MIN{m: A000120(m)=A000120(n) and m>n}. - Reinhard Zumkeller, Aug 15 2009

EXAMPLE

a(6)=9 since 6 has two one-bits (i.e., 6=2+4) and 9 is the next higher integer of binary weight two (7 is weight three and 8 is weight one).

MATHEMATICA

a[n_] := (bw = DigitCount[n, 2, 1]; k = n+1; While[ DigitCount[k, 2, 1] != bw, k++]; k); Table[a[n], {n, 1, 71}](* Jean-François Alcover, Nov 28 2011 *)

PROG

(PARI) a(n)=my(u=bitand(n, -n), v=u+n); (bitxor(v, n)/u)>>2+v \\ Charles R Greathouse IV, Oct 28 2009

(Haskell)

a057168 n = a057168_list !! (n-1)

a057168_list = f 2 $ tail a000120_list where

   f x (z:zs) = (x + length (takeWhile (/= z) zs)) : f (x + 1) zs

-- Reinhard Zumkeller, Aug 26 2012

(PARI) A057168(n)=n+bitxor(n, n+n=bitand(n, -n))\n\4+n \\ M. F. Hasler, Aug 27 2014

CROSSREFS

Cf. A000120, A006519, A057169, A000051, A052548, A140504, A000225, A055010, A007283, A171942.

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

Sequence in context: A110991 A262942 A076990 * A087711 A123128 A057064

Adjacent sequences:  A057165 A057166 A057167 * A057169 A057170 A057171

KEYWORD

easy,nonn,nice,changed

AUTHOR

Marc LeBrun, Sep 14 2000

STATUS

approved

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Last modified June 23 19:21 EDT 2018. Contains 311805 sequences. (Running on oeis4.)