A347470 Least product of any two numbers whose concatenation is n, excluding 0*n for n > 9.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 0, 3, 6, 9, 12, 15, 18, 21, 24, 27, 0, 4, 8, 12, 16, 20, 24, 28, 32, 36, 0, 5, 10, 15, 20, 25, 30, 35, 40, 45, 0, 6, 12, 18, 24, 30, 36, 42, 48, 54, 0, 7, 14, 21, 28, 35, 42, 49, 56, 63, 0, 8, 16, 24, 32, 40, 48, 56, 64, 72, 0, 9, 18, 27, 36, 45, 54, 63, 72, 81, 0, 10, 20, 30, 40, 50, 60, 70, 80, 90, 0, 11, 12

Offset

0,13

Comments

Leading zeros are not allowed: e.g., 101 = concat(10,1) but not concat(1,01). Although 0 is a valid number, we don't allow the trivial decomposition n = concat(0, n) except for the single-digit n < 10, otherwise the minimal product would always be 0.

For n < 111, this sequence coincides with A035930 (same with "largest"), because there is only one possible concatenation, but it differs for n > 111, cf. examples.

Links

Table of n, a(n) for n=0..112.

Eric Angelini, Surface of a number, Sep 01 2021.

Example

The number n = 112 is the concatenation of 1 and 12, or of 11 and 2, with respective products 1*12 = 12 and 11*2 = 22. Hence, a(112) = 12, while A035930(112) = 22.

Prog

(PARI) apply( {A347470(x, t(b, c)=if(c\10<=b%c, b\c*(b%c), c>10, oo))= if(x>9, vecmin(vector(logint(x, 10), j, t(x, 10^j))))}, [0..112])

Crossrefs

Cf. A035930, A007954, A088117, A171765 and A257297.

Sequence in context: A171765 A257297 A035930 * A088117 A349278 A195833

Adjacent sequences: A347467 A347468 A347469 * A347471 A347472 A347473

Keyword

nonn,base

Author

M. F. Hasler, Sep 03 2021

Status

approved