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

0,2

Links

Table of n, a(n) for n=0..62.

Formula

a(n) = 10 + n for 0 < n < 10.

a(n) <= concat(1,n) with equality when n is prime.

Example

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.

Prog

(PARI) apply( {A347471(s, m=oo)=if(s, fordiv(s, d, my(t=eval(Str(d, s/d))); s==A347470(t) && m>t && m=eval(Str(d, s/d))); m)}, [0..111])

Crossrefs

Cf. A347470.

Sequence in context: A261020 A308237 A362023 * A162672 A110403 A119247

Adjacent sequences: A347468 A347469 A347470 * A347472 A347473 A347474

Keyword

nonn,base

Author

M. F. Hasler, Sep 03 2021

Status

approved