A347471 a(n) is the least number k such that n = A347470(k) := least a*b with concat(a,b) = k.
0, 11, 12, 13, 14, 15, 16, 17, 18, 19, 25, 111, 26, 113, 27, 35, 28, 117, 29, 119, 45, 37, 122, 123, 38, 55, 126, 39, 47, 129, 56, 311, 48, 133, 134, 57, 49, 137, 138, 139, 58, 411, 67, 431, 144, 59, 146, 147, 68, 77, 105, 173, 226, 531, 69, 155, 78, 157, 158, 159, 106, 611, 621
Offset: 0
Examples
a(3) = a(1*3) = 13 and similar for 1 <= n <= 9, cf. first formula. a(11) = a(1*11) = 111, a(13) = a(1*13) = 113, a(17) = a(1*17) = 117 etc. according to the second formula with prime n. a(10) = a(2*5) = 25, a(14) = a(2*7) = 27, a(15) = a(3*5) = 35 etc. for semiprime indices; in these cases a(p*q) = concat(p,q) where p is the lexicographic smaller factor, but this is not always the case. a(22) = 122, not concat(11,2), although 11*2 = 22, but the smallest product that can be formed by slicing 112 in two parts is A347470(112) = 1*12 = 12, less than 22. a(93) = a(3*31) = concat(93,1) because concat(1,93) gives 19*3, concat(3,31) gives 33*1 and concat(31,3) gives 3*13 as smaller products.
Crossrefs
Cf. A347470.
Programs
Formula
a(n) = 10 + n for 0 < n < 10.
a(n) <= concat(1,n) with equality when n is prime.