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

2,1

Links

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

Formula

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

Prog

(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

Crossrefs

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

Sequence in context: A321190 A320403 A354067 * A323138 A000252 A078237

Adjacent sequences: A357427 A357428 A357429 * A357431 A357432 A357433

Keyword

nonn,base

Author

Michel Marcus, Sep 28 2022

Extensions

More terms from Rémy Sigrist, Sep 29 2022

Status

approved