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A357273
Integers m whose decimal expansion is a prefix of the concatenation of the divisors of m.
0
1, 11, 12, 124, 135, 1111, 1525, 13515, 124816, 1223462, 12356910, 13919571, 1210320658, 1243162124, 1525125625, 12346121028, 12478141928, 12510153130, 12510254150, 1234689111216, 1351553159265, 1597717414885, 1713913539247, 12356910151830, 13791121336377
OFFSET
1,2
COMMENTS
This is different from A175252 in that the digits to be concatenated can end in the middle of a divisor.
All terms start with the digit 1. - Chai Wah Wu, Sep 23 2022
a(26) > 10^14. - Giovanni Resta, Oct 20 2022
EXAMPLE
11 is a term since its divisors are 1 and 11 whose concatenation is 111 whose first 2 digits are 11.
1111 is a term since its divisors are 1, 11, 101, and 1111 whose concatenation is 1111011111 whose first 4 digits are 1111.
MATHEMATICA
q[n_] := (Join @@ IntegerDigits @ Divisors[n])[[1 ;; Length @ (d = IntegerDigits[n])]] == d; Select[Range[1.3*10^6], q] (* Amiram Eldar, Sep 22 2022 *)
PROG
(PARI) f(n) = my(s=""); fordiv(n, d, s = concat(s, Str(d))); s; \\ A037278
isok(k) = if (k==1, 1, my(v=strsplit(f(k), Str(k))); (v[1] == ""));
(Python)
from sympy import divisors
def ok(n): return "".join(str(d) for d in divisors(n)).startswith(str(n))
print([k for k in range(10**5) if ok(k)]) # Michael S. Branicky, Sep 22 2022
(Python)
from itertools import count, islice
from sympy import divisors
def A357273_gen(): # generator of terms
yield 1
for n in count(1):
r = str(n)
if n&1 or r.startswith('2'):
m = 10**(c:=len(r))+n
s, sm = '', str(m)
for d in divisors(m):
s += str(d)
if len(s) >= c+1:
break
if s.startswith(sm):
yield m
A357273_list = list(islice(A357273_gen(), 10)) # Chai Wah Wu, Sep 23 2022
CROSSREFS
Cf. A037278, A175252 (a subsequence).
Cf. A004022 (a subsequence).
Subsequence of A131835.
Sequence in context: A108218 A038326 A249312 * A041059 A041260 A109665
KEYWORD
nonn,base
AUTHOR
Michel Marcus, Sep 22 2022
EXTENSIONS
a(16)-a(25) from Giovanni Resta, Oct 20 2022
STATUS
approved