A102489 -id:A102489 - cp's OEIS frontend

A090725 Primes whose representation in base 16 has no alphabetic characters.

2, 3, 5, 7, 17, 19, 23, 37, 41, 53, 67, 71, 73, 83, 89, 97, 101, 103, 113, 131, 137, 149, 151, 257, 263, 277, 281, 293, 307, 311, 313, 337, 353, 359, 373, 389, 401, 409, 521, 547, 563, 569, 577, 593, 599, 601, 613, 617, 631, 641, 643, 647, 659, 661, 769, 773

Offset: 1

Cino Hilliard, Jan 18 2004

Subsequence of primes of A102489. - Michel Marcus, Mar 05 2016

Zak Seidov, Table of n, a(n) for n = 1..1000

Cf. A102489.

Select[Prime[Range[400]], Max[IntegerDigits[#, 16]] < 10 & ] (* Zak Seidov, Mar 04 2016 *)

isok(n) = isprime(n) && (vecmax(digits(n, 16)) < 10); \\ Michel Marcus, Mar 05 2016

Better definition from Omar E. Pol, Dec 24 2008

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

A347295 a(n) = 1 + (a(n-1) interpreted as a hexadecimal number); a(1)=1.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 17, 24, 37, 56, 87, 136, 311, 786, 1927, 6440, 25665, 153190, 1388945, 20482374, 541598581, 22571222402, 2359835108355, 621877794997078, 441783186122961017, 1256072821702542102552, 22166920289514371672974675

Offset: 1

Divyanand Valsan, Jan 23 2022

a(1)=1, and each subsequent term is obtained by interpreting the previous term as a hexadecimal number, converting it into decimal, and incrementing by 1.

This same procedure can be applied to create other base-switch sequences, e.g., between hexadecimal and octal or between decimal and octal. The base b1 in which a(n-1) is interpreted must be larger than the base b2 into which it is converted; otherwise, the b1-th term will be b1 written in base b2, which will not be a valid base-b1 expansion (e.g., with b1=10 and b2=16, we would obtain a(10)="A", which is not a valid decimal number).

			a(1)=1;
1_16 = 1_10; 1 + 1 = 2 = a(2);
2_16 = 2_10; 2 + 1 = 3 = a(3);
...
This will continue till a(10)=10, when base differences start to have an effect.
10_16 = 16_10; 16 + 1 = 17 = a(11);
17_16 = 23_10; 23 + 1 = 24 = a(12);
24_16 = 36_10; 36 + 1 = 37 = a(13);
37_16 = 55_10; 55 + 1 = 56 = a(14).

Cf. A102489.

NestList[FromDigits[IntegerDigits[#], 16] + 1 &, 1, 30] (* Amiram Eldar, Jan 23 2022 *)

#Hex-dec switch
seq=[]
seq.append(1)
print(seq[0])
for i in range(1,50):
    dec=int(str(seq[i-1]), 16)
    dec=dec+1
    seq.append(dec)
print(seq)

a(n) = A102489(a(n-1)) + 1. - Jon E. Schoenfield, Jan 23 2022

Limit_{n->infinity} log(a(n))/log_10(16)^n = 0.180064331228631629088182553063.... - Jon E. Schoenfield, Jan 23 2022

cp's OEIS Frontend

A090725 Primes whose representation in base 16 has no alphabetic characters.

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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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A347295 a(n) = 1 + (a(n-1) interpreted as a hexadecimal number); a(1)=1.

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Mathematica

Python

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