A309440 The number of digits of the greatest product from addends that sum up to 10^n.

1, 2, 16, 160, 1591, 15905, 159041, 1590405, 15904042, 159040419, 1590404183, 15904041824, 159040418240, 1590404182399, 15904041823989, 159040418239888, 1590404182398875, 15904041823988748, 159040418239887480, 1590404182398874791, 15904041823988747910, 159040418239887479099

Offset

0,2

Links

Table of n, a(n) for n=0..21.

Formula

a(n) = 1 + floor(log_10(36) + 10*log_10(27)*R_(n-1)), R_k being the k-th repunit, i.e., 111...111 with only digit 1 appearing k times.

Example

The greatest product of numbers that sum up to 10 is 2*2*3*3 = 36 which has 2 digits. Thus a(1) = 2.
The greatest product of numbers that sum up to 100 is 2*2*3^(32) ~ 7.4*10^15 which has 16 digits. Hence a(2) = 16.
The greatest product of numbers that sum up to 1000 is 2*2*3^(332) ~ 1.0*10^159 which has 160 digits. Therefore a(3) = 160.

Prog

(PARI) a(n) = 1 + floor(log(4)/log(10) + ((10^n-1)/3-1)*log(3)/log(10)); \\ Jinyuan Wang, Aug 03 2019

Crossrefs

Cf. A000792.

Sequence in context: A009518 A052674 A259706 * A226012 A011552 A326362

Adjacent sequences: A309437 A309438 A309439 * A309441 A309442 A309443

Keyword

nonn,base

Author

Lekraj Beedassy, Aug 03 2019

Status

approved