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A362023
a(n) is the least positive integer whose decimal expansion is the concatenation of the decimal expansions of two numbers whose product is n.
2
11, 12, 13, 14, 15, 16, 17, 18, 19, 25, 111, 26, 113, 27, 35, 28, 117, 29, 119, 45, 37, 112, 123, 38, 55, 126, 39, 47, 129, 56, 131, 48, 113, 134, 57, 49, 137, 138, 133, 58, 141, 67, 143, 114, 59, 146, 147, 68, 77, 105, 151, 134, 153, 69, 115, 78, 157, 158
OFFSET
1,1
COMMENTS
For any prime number p, a(p) is the least of the concatenation of p with 1 or the concatenation of 1 with p.
LINKS
FORMULA
a(n) <= 10*n + 1.
a(n) <= 10^A055642(n) + n.
a(n) = Min_{d | n} A067574(n/d, d).
EXAMPLE
The first terms, alongside an appropriate way to split them into two factors, are:
n a(n) a(n)
-- ---- ----
1 11 1*1
2 12 1*2
3 13 1*3
4 14 1*4
5 15 1*5
6 16 1*6
7 17 1*7
8 18 1*8
9 19 1*9
10 25 2*5
11 111 11*1
12 26 2*6
13 113 1*13
14 27 2*7
15 35 3*5
MATHEMATICA
Table[Min@ Map[FromDigits[Join @@ #] &, Join @@ {#, Reverse /@ #}] &@ Map[IntegerDigits[#] &, Transpose@{#, n/#}, {2}] &@ TakeWhile[Divisors[n], # <= Sqrt[n] &], {n, 60}] (* Michael De Vlieger, Apr 07 2023 *)
PROG
(PARI) a(n, base = 10) = { my (v = oo); fordiv (n, d, v = min(v, n/d * base^#digits(d, base) + d); ); return (v); }
(Python)
from sympy import divisors
def a(n): return min(int(str(d)+str(n//d)) for d in divisors(n))
print([a(n) for n in range(1, 61)]) # Michael S. Branicky, Apr 05 2023
CROSSREFS
Cf. A055642, A067574, A347471, A362022 (binary variant).
Sequence in context: A284062 A261020 A308237 * A347471 A162672 A110403
KEYWORD
nonn,base
AUTHOR
Rémy Sigrist, Apr 05 2023
STATUS
approved