

A043320


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


15



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
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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 base256 digits are 0x00, 0x11, 0x22,... or 0xFF, in hex notation, and no two adjacent base256 digits are equal.) Thus, these numbers are divisible by 0x11 = 17, and the result of the division is a number which has no other base256 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


CROSSREFS

Cf. A043307  A043319, A043291, A033001  A033014, A033015  A033029.
Sequence in context: A132032 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



