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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.

%I A362023 #13 Apr 07 2023 10:51:34
%S A362023 11,12,13,14,15,16,17,18,19,25,111,26,113,27,35,28,117,29,119,45,37,
%T A362023 112,123,38,55,126,39,47,129,56,131,48,113,134,57,49,137,138,133,58,
%U A362023 141,67,143,114,59,146,147,68,77,105,151,134,153,69,115,78,157,158
%N 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.
%C A362023 For any prime number p, a(p) is the least of the concatenation of p with 1 or the concatenation of 1 with p.
%H A362023 Michael De Vlieger, <a href="/A362023/b362023.txt">Table of n, a(n) for n = 1..10000</a>
%F A362023 a(n) <= 10*n + 1.
%F A362023 a(n) <= 10^A055642(n) + n.
%F A362023 a(n) = Min_{d | n} A067574(n/d, d).
%e A362023 The first terms, alongside an appropriate way to split them into two factors, are:
%e A362023   n   a(n)  a(n)
%e A362023   --  ----  ----
%e A362023    1    11   1*1
%e A362023    2    12   1*2
%e A362023    3    13   1*3
%e A362023    4    14   1*4
%e A362023    5    15   1*5
%e A362023    6    16   1*6
%e A362023    7    17   1*7
%e A362023    8    18   1*8
%e A362023    9    19   1*9
%e A362023   10    25   2*5
%e A362023   11   111  11*1
%e A362023   12    26   2*6
%e A362023   13   113  1*13
%e A362023   14    27   2*7
%e A362023   15    35   3*5
%t A362023 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 *)
%o A362023 (PARI) a(n, base = 10) = { my (v = oo); fordiv (n, d, v = min(v, n/d * base^#digits(d, base) + d);); return (v); }
%o A362023 (Python)
%o A362023 from sympy import divisors
%o A362023 def a(n): return min(int(str(d)+str(n//d)) for d in divisors(n))
%o A362023 print([a(n) for n in range(1, 61)]) # _Michael S. Branicky_, Apr 05 2023
%Y A362023 Cf. A055642, A067574, A347471, A362022 (binary variant).
%K A362023 nonn,base
%O A362023 1,1
%A A362023 _Rémy Sigrist_, Apr 05 2023