OFFSET
0,3
COMMENTS
List of numbers in base-16 representation that can be written with decimal digits.
Early in the sequence there are blocks recurring as a(n) = a(n-10)+16, but this pattern starts to fail when we reach 160, 161, ... with hex-representations A0, A1, ... which cannot be written with decimal digits. - Rick L. Shepherd, Jun 08 2012
Binary Coded Decimal (BCD) codes, common in electronics, when interpreted as plain binary-coded integers. For example, number 39 is BCD coded in two nibbles as 0011 1001 which is the binary expansion of 57; hence, taking into account the offset, a(1+39) = 57. - Stanislav Sykora, Jun 09 2012
Integers that avoid letters in their hexadecimal expansion. - Eliora Ben-Gurion, Aug 28 2019
LINKS
Reinhard Zumkeller, Table of n, a(n) for n = 0..9999
Eric Weisstein's World of Mathematics, Hexadecimal
FORMULA
a(n) - a(n-1) = (2*16^A122840(n) + 3)/5. - Robert Israel, Aug 30 2015
EXAMPLE
10 in decimal is 16 in base 16, so a(10)=16.
MAPLE
o10:= n -> min(padic:-ordp(n, 2), padic:-ordp(n, 5)):
d:= [0, seq((2*16^o10(n)+3)/5, n=1..1000)]:
ListTools:-PartialSums(d); # Robert Israel, Aug 30 2015
MATHEMATICA
Table[FromDigits[IntegerDigits[n], 16], {n, 0, 70}] (* Ivan Neretin, Aug 12 2015 *)
PROG
(Haskell)
import Data.Maybe (fromJust, mapMaybe)
a102489 n = a102489_list !! (n-1)
a102489_list = mapMaybe dhex [0..] where
dhex 0 = Just 0
dhex x | d > 9 || y == Nothing = Nothing
| otherwise = Just $ 16 * fromJust y + d
where (x', d) = divMod x 16; y = dhex x'
-- Reinhard Zumkeller, Jul 06 2012
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Reinhard Zumkeller, Jan 12 2005
EXTENSIONS
Edited by N. J. A. Sloane, Feb 08 2014 (changed definition, moved old definition to comment, changed offset and b-file).
STATUS
approved