A140977 a(n) is the smallest integer > n that has the same number of (nonleading) zeros in its binary representation as n has.

3, 5, 7, 9, 6, 11, 15, 17, 10, 12, 13, 19, 14, 23, 31, 33, 18, 20, 21, 24, 22, 25, 27, 35, 26, 28, 29, 39, 30, 47, 63, 65, 34, 36, 37, 40, 38, 41, 43, 48, 42, 44, 45, 49, 46, 51, 55, 67, 50, 52, 53, 56, 54, 57, 59, 71, 58, 60, 61, 79, 62, 95, 127, 129, 66, 68, 69, 72, 70, 73, 75

Offset

1,1

Comments

Permutation of the non-binary powers, cf. A057716. - Reinhard Zumkeller, Aug 15 2010

Links

R. Zumkeller, Table of n, a(n) for n = 1..1000

Rémy Sigrist, PARI program for A140977

Example

4 in binary is 100, which has 2 zeros. Checking the binary representations of the integers > 4: 5 = 101 in binary, which has one 0. 6 = 110 in binary, which has one 0. 7 = 111 in binary, which has zero 0's. 8 = 1000 in binary, which has three 0's. But 9 = 1001 in binary, which has two 0's, the same number of zeros that 4 (= 100 in binary) has. So a(4) = 9.

Mathematica

a = {}; For[n = 1, n < 100, n++, i = n + 1; While[ ! DigitCount[i, 2, 0] == DigitCount[n, 2, 0], i++ ]; AppendTo[a, i]]; a (* Stefan Steinerberger, Aug 25 2008 *)
snz[n_]:=Module[{dn=DigitCount[n, 2, 0], k=n+1}, While[DigitCount[k, 2, 0] != dn, k++]; k]; Array[snz, 100] (* Harvey P. Dale, May 15 2015 *)

Prog

(PARI) See Links section.

Crossrefs

Cf. A057168, A023416.

Sequence in context: A213542 A029657 A122641 * A161821 A317509 A139083

Adjacent sequences: A140974 A140975 A140976 * A140978 A140979 A140980

Keyword

base,nonn

Author

Leroy Quet, Aug 17 2008

Extensions

More terms from Stefan Steinerberger, Aug 25 2008

Status

approved