A043320 Numbers which, written in base 256, have all digits less than 16 and no two adjacent digits equal.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 256, 258, 259, 260, 261, 262, 263, 264, 265, 266, 267, 268, 269, 270, 271, 512, 513, 515, 516, 517, 518, 519, 520, 521, 522, 523, 524, 525, 526, 527, 768, 769, 770, 772, 773, 774

Offset

1,2

Comments

Sequence A033014 consists of the numbers that have all base 16 digits repeated *exactly* twice. (This is equivalent to say that the base-256 digits are 0x00, 0x11, 0x22,... or 0xFF, in hex notation, and no two adjacent base-256 digits are equal.) Thus, these numbers are divisible by 0x11 = 17, and the result of the division is a number which has no other base-256 digits than 0x00, 0x01,... or 0x0F, and no two adjacent digits equal. Conversely, it is clear that exactly these numbers are terms of A033014 when multiplied by 17 = 0x11. - M. F. Hasler, Feb 05 2014

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1800

Formula

a(n) = A033014(n)/17. [This was initially the definition of the sequence. - M. F. Hasler, Feb 03 2014]

Mathematica

Select[Range[20000], Union[Length/@Split[IntegerDigits[#, 16]]]=={2}&]/17 (* Vincenzo Librandi, Feb 06 2014 *)

Prog

(PARI) is_A043320(n)={(n=[n])&&!until(!n[1], ((n=divrem(n[1], 256))[2]<16 && n[1]%16!=n[2])||return)} \\ M. F. Hasler, Feb 03 2014
(Python)
from itertools import count, islice, groupby
def A043320_gen(startvalue=1): # generator of terms >= startvalue
    return filter(lambda n:set(len(list(g)) for k, g in groupby(hex(17*n)[2:]))=={2}, count(max(startvalue, 1)))
A043320_list = list(islice(A043320_gen(), 20)) # Chai Wah Wu, Mar 10 2023

Crossrefs

Cf. A043307 - A043319, A043291, A033001 - A033014, A033015 - A033029.

Sequence in context: A341709 A055645 A262545 * A044917 A246337 A161953

Adjacent sequences: A043317 A043318 A043319 * A043321 A043322 A043323

Keyword

nonn,base

Author

Clark Kimberling

Extensions

New definition by M. F. Hasler, Feb 03 2014

Status

approved