A102493 -id:A102493 - cp's OEIS frontend

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

Reinhard Zumkeller, Jan 12 2005

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

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

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

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

Cf. A090725 (the subsequence of primes).

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

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

Table[FromDigits[IntegerDigits[n], 16], {n, 0, 70}] (* Ivan Neretin, Aug 12 2015 *)

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

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

A102487 Numbers in base-12 representation that can be written with decimal digits.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 84, 85, 86

Offset: 1

Reinhard Zumkeller, Jan 12 2005

Numbers that are only in this sequence or only in A039274 but not in both are n= 131, 142, 275, 286, 419, 430 etc: see A039558. [From R. J. Mathar, Aug 30 2008]

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Duodecimal
Wikipedia, Duodecimal

Complement of A102488; A102489, A102491, A102493.

Cf. A033048 (subsequence).

import Data.List (unfoldr)
a102487 n = a102487_list !! (n-1)
a102487_list = filter (all (< 10) . unfoldr (\x ->
   if x == 0 then Nothing else Just $ swap $ divMod x 12)) [0..]
-- Reinhard Zumkeller, Apr 18 2011

fQ[n_] := Last@ Union@ IntegerDigits[n, 12] < 10; Select[ Range[0, 86], fQ] (* Robert G. Wilson v, Apr 17 2012 *)

{for(testn=0,87,
lgt=1;
for(i=1,1000,if(12^i > testn,lgt=i;break()));
atst=testn;pasr=1;
for(j=1,lgt,lasd=atst%12;
if(lasd<10,atst=(atst-lasd)/12,pasr=0;break()));
if(pasr==1,print1(testn,", ")))}
\\ Douglas Latimer, Apr 17 2012

A102487_list = [int(str(x), 12) for x in range(10**6)] # Chai Wah Wu, Apr 09 2016

A102491 Numbers whose base-20 representation can be written with decimal digits.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 120, 121, 122, 123, 124, 125, 126

Offset: 1

Reinhard Zumkeller, Jan 12 2005

a(n) = A118761(n) for n<=50. - Reinhard Zumkeller, May 01 2006

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Vigesimal
Wikipedia, Vigesimal

Complement of A102492; Cf. A102487, A102489, A102493. Cf. A037454, A037462, A007091.

import Data.List (unfoldr)
a102491 n = a102491_list !! (n-1)
a102491_list = filter (all (<= 9) . unfoldr
   (\x -> if x == 0 then Nothing else Just $ swap $ divMod x 20)) [0..]
-- Reinhard Zumkeller, Jun 27 2013

seq(n + (1/2)*add(20^k*floor(n/10^k), k = 1..floor(ln(n)/ln(10))), n = 1..100); # Peter Bala, Dec 01 2016

Select[Range@ 126, Total@ Take[Most@ DigitCount[#, 20], -10] == 0 &] (* Michael De Vlieger, Apr 09 2016 *)

isok(n) = (n==0) || ((d=digits(n, 20)) && (vecmax(d) < 10)); \\ Michel Marcus, Apr 09 2016

a(n) = fromdigits(digits(n-1),20) \\ Ruud H.G. van Tol, Dec 08 2022

A102491_list = [int(str(x), 20) for x in range(10**6)] # Chai Wah Wu, Apr 09 2016

From Peter Bala, Dec 01 2016: (Start)
If n = Sum_{i = 0..m} d(i)*10^i is the decimal expansion of n then a(n+1) = Sum_{i = 0..m} d(i)*20^i.
a(n+1) = n + 1/2*Sum_{k >= 1} 20^k*floor(n/10^k). Cf. A037454, A037462 and A007091.
a(1) = 0; a(n+1) = 20*a(n/10+1) if n == 0 (mod 10) else a(n+1) = a(n) + 1. (End)
G.f. g(x) satisfies g(x) = 20*Sum_{1<=k<=9} x^k*g(x^10)/x^9 + Sum_{1<=k<=9} k*x^(k+1)/(1-x^10). - Robert Israel, Dec 01 2016

A102494 Numbers in base-60 representation that cannot be written with decimal digits.

Original entry on oeis.org

10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88

Offset: 1

Reinhard Zumkeller, Jan 12 2005

			200 = 3*60^1 + 20*60^0 = '3K', therefore 200 is a term.

Mohammad K. Azarian, Meftah al-hesab: A Summary, MJMS, Vol. 12, No. 2, Spring 2000, pp. 75-95. Mathematical Reviews, MR 1 764 526. Zentralblatt MATH, Zbl 1036.01002.
Mohammad K. Azarian, A Summary of Mathematical Works of Ghiyath ud-din Jamshid Kashani, Journal of Recreational Mathematics, Vol. 29(1), pp. 32-42, 1998.

Harvey P. Dale, Table of n, a(n) for n = 1..1000
Eric Weisstein's World of Mathematics, Sexagesimal
Wikipedia, Sexagesimal

Complement of A102493; A102488, A102490, A102492.

import Data.List (unfoldr)
a102494 n = a102494_list !! (n-1)
a102494_list = filter (any (> 9) . unfoldr
   (\x -> if x == 0 then Nothing else Just $ swap $ divMod x 60)) [0..]
-- Reinhard Zumkeller, Jun 27 2013

Select[Range[100],Max[IntegerDigits[#,60]]>9&] (* Harvey P. Dale, Dec 27 2012 *)

cp's OEIS Frontend

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

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A102487 Numbers in base-12 representation that can be written with decimal digits.

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A102491 Numbers whose base-20 representation can be written with decimal digits.

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A102494 Numbers in base-60 representation that cannot be written with decimal digits.

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