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

Author

N. J. A. Sloane, Mar 23 2005

Keywords

• nonn
• easy
• base

Links

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

Crossrefs

Cf. A102370, A103584.

Programs

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 *)

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.

Extensions

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