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A057168
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Next larger integer with same binary weight (number of 1 bits) as n.
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3
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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; internal format)
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OFFSET
| 1,1
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COMMENTS
| Binary weight is given by A000120.
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). [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Aug 18 2008]
a(n) = MIN{m: A000120(m)=A000120(n) and m>n}. [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Aug 15 2009]
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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.
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LINKS
| R. Zumkeller, Table of n, a(n) for n = 1..10000 [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Aug 15 2009]
Beeler, M., Gosper, R. W. and Schroeppel, R., HAKMEM ITEM 175
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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).
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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}](* From Jean-François Alcover, Nov 28 2011 *)
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PROG
| (PARI) a(n)={my(u=bitand(n, -n), v=u+n); (bitxor(v, n)/u)>>2+v};
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CROSSREFS
| Cf. A000120, A006519, A057169.
Sequence in context: A101410 A110991 A076990 * A087711 A123128 A057064
Adjacent sequences: A057165 A057166 A057167 * A057169 A057170 A057171
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KEYWORD
| easy,nonn,nice
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AUTHOR
| Marc LeBrun (mlb(AT)well.com), Sep 14 2000
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EXTENSIONS
| Program and reference from Charles R Greathouse IV (charles.greathouse(AT)case.edu), Oct 28 2009
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