A103543 Consider those values of k for which A102370(k) = k: 0, 4, 8, 16, 20, 24, 32, 36, 40, 48, 52, 56, 64, ... and divide by 4: 0, 1, 2, 4, 5, 6, 8, 9, 10, 12, 13, 14, 16, 17, 18, 20, 21, 22, 24, ...; sequence gives missing numbers.

3, 7, 11, 15, 19, 23, 27, 31, 35, 39, 43, 47, 51, 55, 59, 62, 63, 67, 71, 75, 79, 83, 87, 91, 95, 99, 103, 107, 111, 115, 119, 123, 126, 127, 131, 135, 139, 143, 147, 151, 155, 159, 163, 167, 171, 175, 179, 183, 187, 190, 191, 195, 199, 203, 207, 211, 215, 219, 223

Offset

1,1

Links

Table of n, a(n) for n=1..59.

David Applegate, Benoit Cloitre, Philippe Deléham and N. J. A. Sloane, Sloping binary numbers: a new sequence related to the binary numbers [pdf, ps].

Formula

Numbers of the form 4k+3 together with the terms of A103584.

It is shown in the reference that A102370(k) = k iff n == 0 (mod 4) and n does not belong to any of the arithmetic progressions Q_r := {2^(4r)*j - 4r, j >= 1} for r = 1, 2, 3, ...

In other words, the sequence consists of the numbers of the form j*2^(4k-2) - k for k >=2 and j >= 1.

Mathematica

f[n_] := Block[{k = 1, s = 0, l = Max[2, Floor[Log[2, n + 1] + 2]]}, While[k < l, If[ Mod[n + k, 2^k] == 0, s = s + 2^k]; k++ ]; s]; Complement[ Range[225], Select[ Range[900], f[ # ] == 0 &]/4] (* Robert G. Wilson v, Mar 23 2005 *)

Crossrefs

Cf. A102370, A103584.

Sequence in context: A189534 A179874 A190349 * A172338 A189787 A004767

Adjacent sequences: A103540 A103541 A103542 * A103544 A103545 A103546

Keyword

nonn,easy,base

Author

N. J. A. Sloane, Mar 23 2005

Extensions

More terms from Robert G. Wilson v, Mar 23 2005

Status

approved