A102489 Take the decimal representation of n and read it as if it were written in hexadecimal.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 112

Offset: 0

Author

Reinhard Zumkeller, Jan 12 2005

Keywords

• nonn
• base

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

Examples

			10 in decimal is 16 in base 16, so a(10)=16.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 0..9999
• Eric Weisstein's World of Mathematics, Hexadecimal

Crossrefs

Complement of A102490; A102487, A102491, A102493, A122840.

Cf. A090725 (the subsequence of primes).

Programs

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

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 *)

Formula

a(n) - a(n-1) = (2*16^A122840(n) + 3)/5. - Robert Israel, Aug 30 2015

Extensions

Edited by N. J. A. Sloane, Feb 08 2014 (changed definition, moved old definition to comment, changed offset and b-file).