A380358 Numbers whose binary expansion ends with 11 and does not contain adjacent zeros.

3, 7, 11, 15, 23, 27, 31, 43, 47, 55, 59, 63, 87, 91, 95, 107, 111, 119, 123, 127, 171, 175, 183, 187, 191, 215, 219, 223, 235, 239, 247, 251, 255, 343, 347, 351, 363, 367, 375, 379, 383, 427, 431, 439, 443, 447, 471, 475, 479, 491, 495, 503, 507, 511, 683

Offset

1,1

Comments

The numbers in this sequence appear in the conversion of conventional binary numbers to the canonical signed-digit representation.

References

J. L. Smith and A. Weinberger, "Shortcut Multiplication for Binary Digital Computers", in Methods for High-Speed Addition and Multiplication, National Bureau of Standards Circular 591, Sec. 1, February, 1958, page 21.

Links

Table of n, a(n) for n=1..55.

R. J. Cintra, A note on the conversion of nonnegative integers to the canonical signed-digit representation, arXiv:2501.10908 [eess.SP], 2025.

Formula

a(n) = 2 * A247648(n) + 1.

From Hugo Pfoertner, Feb 07 2025: (Start)

a(n) = 4*A052499(n) - 1.

a(n) = 4*(A365808(n+1) + 1)/3 - 1.

a(n) = 2*(A365809(n) + 1)/3 - 1. (End)

Example

183 is in the sequence because its binary expansion is 10110111.

Mathematica

Select[4*Range[0, 170] + 3, SequencePosition[IntegerDigits[#, 2], {0, 0}] == {} &] (* Amiram Eldar, Feb 05 2025 *)

Prog

(Python)
from itertools import count, islice
def A380358_gen(startvalue=1): # generator of terms >= startvalue
    return filter(lambda n:n&3==3 and not '00' in bin(n), count(max(startvalue, 1)))
A380358_list = list(islice(A380358_gen(), 20)) # Chai Wah Wu, Feb 12 2025

Crossrefs

Cf. A003754, A052499, A247648, A365808, A365809.

Sequence in context: A095100 A036994 A243115 * A394060 A279106 A172306

Adjacent sequences: A380355 A380356 A380357 * A380359 A380360 A380361

Keyword

nonn,base

Author

R. J. Cintra, Jan 22 2025

Status

approved