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A309440 The number of digits of the greatest product from addends that sum up to 10^n. 0
1, 2, 16, 160, 1591, 15905, 159041, 1590405, 15904042, 159040419, 1590404183, 15904041824, 159040418240, 1590404182399, 15904041823989, 159040418239888, 1590404182398875, 15904041823988748, 159040418239887480, 1590404182398874791, 15904041823988747910, 159040418239887479099 (list; graph; refs; listen; history; text; internal format)
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

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Last modified April 4 05:34 EDT 2020. Contains 333212 sequences. (Running on oeis4.)