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.
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
Examples
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
Links
- Michael De Vlieger, Table of n, a(n) for n = 1..10000
Programs
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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 *) -
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
Comments