OFFSET
1,1
COMMENTS
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
LINKS
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.
EXAMPLE
480_10 = 1e0_16 and 1e0 = 1 in E notation.
739_10 = 2e3_16 and 2e3 = 2000_10 in E notation.
PROG
(C++)
#include <iostream>
#include <string>
using namespace std;
int main()
{
int n = 0; //integer to check
char hexRepresentation[12];
for (int i = 0; i < 100; ) //integers found (first 100)
{
sprintf(hexRepresentation, "%x", n); //get hex representation
char* foundE = strchr(hexRepresentation, 'e'); //look for letter e
if (foundE != NULL && //at least one e
hexRepresentation != foundE && //not the first digit
strpbrk(hexRepresentation, "abcdef") == foundE && //e is not first alpha
strlen(foundE) != 1 && //something after the e
strpbrk(foundE + sizeof(char), "abcdef") == NULL) //no alpha after the e
{
cout << n << "\n"; //output n
i++; //discovered an integer
}
n++; //check next value
}
}
(Python)
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
(C)
#include <stdbool.h>
#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
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Adam J.T. Partridge, Sep 16 2015
STATUS
approved