cp's OEIS Frontend

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

%I A262222 #48 Sep 29 2023 10:19:55
%S A262222 480,481,482,483,484,485,486,487,488,489,736,737,738,739,740,741,742,
%T A262222 743,744,745,992,993,994,995,996,997,998,999,1000,1001,1248,1249,1250,
%U A262222 1251,1252,1253,1254,1255,1256,1257,1504,1505,1506,1507,1508,1509,1510,1511
%N A262222 Decimal representations of hexadecimal numbers that can be misinterpreted as decimal numbers in scientific E notation.
%C A262222 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.
%C A262222 These numbers are especially troublesome when importing hexadecimal numbers from CSV files into Microsoft Excel.
%C A262222 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.
%C A262222 Numbers whose hexadecimal representation matches the regular expression [1-9][0-9]*e[0-9]+. - _Eric M. Schmidt_, Sep 28 2023
%H A262222 Christian Perfect, <a href="/A262222/b262222.txt">Table of n, a(n) for n = 1..99999</a>
%H A262222 Microsoft Community, <a href="http://answers.microsoft.com/en-us/office/forum/office_2007-excel/disabling-scientific-notation/943b8103-8c50-451d-8037-c697422e2307">Unable to disable scientific notation in Microsoft Excel</a>.
%H A262222 Wikipedia, <a href="https://en.wikipedia.org/wiki/Scientific_notation#E_notation">Scientific E notation</a>.
%e A262222 480_10 = 1e0_16 and 1e0 = 1 in E notation.
%e A262222 739_10 = 2e3_16 and 2e3 = 2000_10 in E notation.
%o A262222 (C++)
%o A262222 #include <iostream>
%o A262222 #include <string>
%o A262222 using namespace std;
%o A262222 int main()
%o A262222 {
%o A262222   int n = 0;                  //integer to check
%o A262222   char hexRepresentation[12];
%o A262222   for (int i = 0; i < 100;)   //integers found (first 100)
%o A262222   {
%o A262222     sprintf(hexRepresentation, "%x", n);              //get hex representation
%o A262222     char* foundE = strchr(hexRepresentation, 'e');    //look for letter e
%o A262222     if (foundE != NULL &&                             //at least one e
%o A262222     hexRepresentation != foundE &&                    //not the first digit
%o A262222     strpbrk(hexRepresentation, "abcdef") == foundE && //e is not first alpha
%o A262222     strlen(foundE) != 1 &&                            //something after the e
%o A262222     strpbrk(foundE + sizeof(char), "abcdef") == NULL) //no alpha after the e
%o A262222     {
%o A262222       cout << n << "\n";    //output n
%o A262222       i++;                  //discovered an integer
%o A262222     }
%o A262222     n++;                    //check next value
%o A262222   }
%o A262222 }
%o A262222 (Python)
%o A262222 from itertools import count,product
%o A262222 # every string of d characters with exactly one 'e' in it, and all the other characters digits 0-9, in ascending lexicographic order
%o A262222 def mids(d):
%o A262222     if d<1:
%o A262222         raise Exception("d<1")
%o A262222     if d==1:
%o A262222         yield 'e'
%o A262222         return
%o A262222     for i in range(0,10):
%o A262222         for m in mids(d-1):
%o A262222             yield str(i)+m
%o A262222     for i in range(10**(d-1)):
%o A262222         yield 'e'+str(i).zfill(d-1)
%o A262222 def a_generator():
%o A262222     for d in count(1):
%o A262222         for start in range(1,10): # for each leading digit 1-9
%o A262222             for mid in mids(d): # for all possible middles made of d characters, containing exactly one 'e'
%o A262222                 for end in range(10): #for each possible final digit, 0-9
%o A262222                     s = '{}{}{}'.format(start,''.join(mid),end)
%o A262222                     i = int(s,16)
%o A262222                     yield i
%o A262222 a262222 = a_generator()
%o A262222 [next(a262222) for _ in range(48)] # _Christian Perfect_, Oct 20 2015
%o A262222 (C)
%o A262222 #include <stdbool.h>
%o A262222 #define DIGIT_E 14
%o A262222 bool isA262222(int k)
%o A262222 {
%o A262222     if (k <= 0 || k % 16 == DIGIT_E) return false;
%o A262222     bool foundE = false;
%o A262222     int digit;
%o A262222     while (k > 0) {
%o A262222         digit = k % 16;
%o A262222         if (digit == DIGIT_E) {
%o A262222             if (foundE) return false;
%o A262222             foundE = true;
%o A262222         }
%o A262222         else if (digit > 9) return false;
%o A262222         k /= 16;
%o A262222     }
%o A262222     return foundE && digit != DIGIT_E;
%o A262222 } // _Eric M. Schmidt_, Sep 28 2023
%Y A262222 A subset of A102490.
%K A262222 nonn,base
%O A262222 1,1
%A A262222 _Adam J.T. Partridge_, Sep 16 2015