A102490 -id:A102490 - 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).

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 *)

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 *)

A262222 Decimal representations of hexadecimal numbers that can be misinterpreted as decimal numbers in scientific E notation.

Original entry on oeis.org

480, 481, 482, 483, 484, 485, 486, 487, 488, 489, 736, 737, 738, 739, 740, 741, 742, 743, 744, 745, 992, 993, 994, 995, 996, 997, 998, 999, 1000, 1001, 1248, 1249, 1250, 1251, 1252, 1253, 1254, 1255, 1256, 1257, 1504, 1505, 1506, 1507, 1508, 1509, 1510, 1511

Offset: 1

Adam J.T. Partridge, Sep 16 2015

Hexadecimal numbers containing no alpha digits other than a single "e", where the "e" is not the first or last digit (e.g., 3e12), may be misinterpreted as numbers in scientific E notation.
These numbers are especially troublesome when importing hexadecimal numbers from CSV files into Microsoft Excel.
These numbers can be written as 16^(i+1)a + 14*16^i + b where a and b are members of A102489 with a>0, b<16^i and i>0.
Numbers whose hexadecimal representation matches the regular expression [1-9][0-9]*e[0-9]+. - Eric M. Schmidt, Sep 28 2023

			480_10 = 1e0_16 and 1e0 = 1 in E notation.
739_10 = 2e3_16 and 2e3 = 2000_10 in E notation.

Christian Perfect, Table of n, a(n) for n = 1..99999
Microsoft Community, Unable to disable scientific notation in Microsoft Excel.
Wikipedia, Scientific E notation.

A subset of A102490.

#include 
#define DIGIT_E 14
bool isA262222(int k)
{
    if (k <= 0 || k % 16 == DIGIT_E) return false;
    bool foundE = false;
    int digit;
    while (k > 0) {
        digit = k % 16;
        if (digit == DIGIT_E) {
            if (foundE) return false;
            foundE = true;
        }
        else if (digit > 9) return false;
        k /= 16;
    }
    return foundE && digit != DIGIT_E;
} // Eric M. Schmidt, Sep 28 2023

from itertools import count,product
# every string of d characters with exactly one 'e' in it, and all the other characters digits 0-9, in ascending lexicographic order
def mids(d):
    if d<1:
        raise Exception("d<1")
    if d==1:
        yield 'e'
        return
    for i in range(0,10):
        for m in mids(d-1):
            yield str(i)+m
    for i in range(10**(d-1)):
        yield 'e'+str(i).zfill(d-1)
def a_generator():
    for d in count(1):
        for start in range(1,10): # for each leading digit 1-9
            for mid in mids(d): # for all possible middles made of d characters, containing exactly one 'e'
                for end in range(10): #for each possible final digit, 0-9
                    s = '{}{}{}'.format(start,''.join(mid),end)
                    i = int(s,16)
                    yield i
a262222 = a_generator()
[next(a262222) for  in range(48)] # _Christian Perfect, Oct 20 2015

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

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

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A262222 Decimal representations of hexadecimal numbers that can be misinterpreted as decimal numbers in scientific E notation.

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