A357430 a(n) is the least integer > 1 such that its digit representation in base n is equal to the digit representation in base n of the initial terms of its set of divisors in increasing order.

6, 48, 6, 182, 8, 66, 10, 102, 12, 1586, 14, 198, 16, 258, 18, 345, 20, 402, 22, 486, 24, 306484, 26, 678, 28, 786, 30, 26102, 32, 1026, 34, 1158, 36, 1335, 38, 1446, 40, 1602, 42, 204741669824, 44, 1938, 46, 2118, 48, 2355, 50, 2502, 52, 2706, 54, 8199524, 56

Offset: 2

Author

Michel Marcus, Sep 28 2022

Keywords

• nonn
• base

Links

• Rémy Sigrist, Table of n, a(n) for n = 2..148

Crossrefs

Cf. A175252 (base 10), A357428 (base 2), A357429 (base 3).

Programs

PARI

isok(k, b) = my(s=[]); fordiv(k, d, s=concat(s, digits(d, b)); if (fromdigits(s, b)==k, return(1)); if (fromdigits(s, b)> k, return(0)));
a(n) = my(k=2); while(! isok(k, n), k++); k;

Python

from sympy import divisors
from sympy.ntheory import digits
from itertools import count, islice
def ok(n, b):
    target, s = digits(n, b)[1:], []
    if target[0] != 1: return False
    for d in divisors(n):
        s += digits(d, b)[1:]
        if len(s) >= len(target): return s == target
        elif not target[:len(s)] == s: return False
def a(n):
    return next(i for d in count(1) for i in range(n**d, 2*n**d) if ok(i, n))
print([a(n) for n in range(2, 41)]) # Michael S. Branicky, Oct 05 2022

Formula

a(2*n) = 2*n + 2 for any n > 1. - Rémy Sigrist, Sep 29 2022

Extensions

More terms from Rémy Sigrist, Sep 29 2022