A102494 -id:A102494 - cp's OEIS frontend

A102490 Numbers in base-16 representation that cannot be written with decimal digits.

10, 11, 12, 13, 14, 15, 26, 27, 28, 29, 30, 31, 42, 43, 44, 45, 46, 47, 58, 59, 60, 61, 62, 63, 74, 75, 76, 77, 78, 79, 90, 91, 92, 93, 94, 95, 106, 107, 108, 109, 110, 111, 122, 123, 124, 125, 126, 127, 138, 139, 140, 141, 142, 143, 154, 155, 156, 157, 158, 159, 160

Offset: 1

Reinhard Zumkeller, Jan 12 2005

			42 = 2*16^1 + 10*16^0 = '2A', therefore 42 is a term.

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

Complement of A102489; A102488, A102492, A102494.

import Data.List (unfoldr)
a102490 n = a102490_list !! (n-1)
a102490_list = filter (any (> 9) . unfoldr
   (\x -> if x == 0 then Nothing else Just $ swap $ divMod x 16)) [0..]
-- Reinhard Zumkeller, Jun 27 2013

Select[Range[200],IntegerLength[Max[IntegerDigits[#,16]]]>1&] (* Harvey P. Dale, Jun 12 2020 *)

def ok(n): return any(hd > '9' for hd in hex(n)[2:])
print(list(filter(ok, range(161)))) # Michael S. Branicky, Oct 11 2021

A102488 Numbers in base-12 representation that cannot be written with decimal digits.

Original entry on oeis.org

10, 11, 22, 23, 34, 35, 46, 47, 58, 59, 70, 71, 82, 83, 94, 95, 106, 107, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 154, 155, 166, 167, 178, 179, 190, 191, 202, 203, 214

Offset: 1

Reinhard Zumkeller, Jan 12 2005

			143 = 11*12^1 + 11*12^0 = 'BB', therefore 143 is a term.

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

Complement of A102487; A102490, A102492, A102494.

import Data.List (unfoldr)
a102488 n = a102488_list !! (n-1)
a102488_list = filter (any (> 9) . unfoldr (\x ->
   if x == 0 then Nothing else Just $ swap $ divMod x 12)) [1..]
-- Reinhard Zumkeller, Apr 18 2011

Select[Range[250],Max[IntegerDigits[#,12]]>9&] (* Harvey P. Dale, Oct 20 2020 *)

A102492 Numbers in base-20 representation that cannot be written with decimal digits.

Original entry on oeis.org

10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 130, 131, 132, 133

Offset: 1

Reinhard Zumkeller, Jan 12 2005

			112 = 5*20^1 + 12*20^0 = '5C', therefore 112 is a term.

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

Complement of A102491; A102488, A102490, A102494.

import Data.List (unfoldr)
a102492 n = a102492_list !! (n-1)
a102492_list = filter (any (> 9) . unfoldr
   (\x -> if x == 0 then Nothing else Just $ swap $ divMod x 20)) [0..]
-- Reinhard Zumkeller, Jun 27 2013

Select[Range[150],Max[IntegerDigits[#,20]]>9&] (* Harvey P. Dale, Mar 27 2021 *)

A102493 Numbers in base-60 representation that can be written with decimal digits.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 240, 241, 242, 243, 244, 245, 246, 247, 248, 249, 300, 301, 302, 303, 304, 305, 306, 307, 308

Offset: 1

Reinhard Zumkeller, Jan 12 2005

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.

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

Complement of A102494; A102487, A102489, A102491.

import Data.List (unfoldr)
a102493 n = a102493_list !! (n-1)
a102493_list = filter (all (<= 9) . unfoldr
   (\x -> if x == 0 then Nothing else Just $ swap $ divMod x 60)) [0..]
-- Reinhard Zumkeller, Jun 27 2013

Table[Range[60n,60n+9],{n,0,6}]//Flatten (* Harvey P. Dale, Jul 06 2024 *)

cp's OEIS Frontend

A102490 Numbers in base-16 representation that cannot be written with decimal digits.

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A102488 Numbers in base-12 representation that cannot be written with decimal digits.

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A102492 Numbers in base-20 representation that cannot be written with decimal digits.

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A102493 Numbers in base-60 representation that can be written with decimal digits.

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Mathematica