A083178 Numbers with a digit sum of n and a maximum product of digits. In case of two identical products choose the largest number.

1, 2, 3, 22, 32, 33, 322, 332, 333, 3322, 3332, 3333, 33322, 33332, 33333, 333322, 333332, 333333, 3333322, 3333332, 3333333, 33333322, 33333332, 33333333, 333333322, 333333332, 333333333, 3333333322, 3333333332, 3333333333

Offset

1,2

Comments

The corresponding maximum product is A000792(n). - Lekraj Beedassy, Nov 13 2009

Except for the first term, terms in the sequence are exactly those numbers formed by sequence of digits 3 followed by either zero, one or two digits 2. - Chai Wah Wu, Dec 11 2015

Links

Table of n, a(n) for n=1..30.

Formula

Conjecture: a(n) = 10*a(n-3)+a(n-6)-10*a(n-9) for n>10. - Colin Barker, Oct 14 2014

Empirical g.f.: x*(90*x^6+10*x^4+11*x^3+3*x^2+2*x+1) / ((x-1)*(x^2+x+1)*(10*x^3-1)). - Colin Barker, Oct 14 2014

For n > 7, a(n) = 11*a(n-3)-10*a(n-6). For n > 4, a(n-3) + 3*10^(floor((n-1)/3)). For n > 1, (2*10^(floor((n+2)/3))+(63*m^2-129*m-2))/6, where m is the least nonnegative residue of n mod 3. - Chai Wah Wu, Dec 11 2015

Prog

(Python)
from __future__ import division
def A083178(n):
    return 1 if n == 1 else (2*10**((n+2)//3)+(63*(n%3)**2-129*(n%3)-2))//6 # Chai Wah Wu, Dec 11 2015

Crossrefs

Cf. A000792.

Sequence in context: A248907 A062921 A298470 * A268866 A154254 A264696

Adjacent sequences: A083175 A083176 A083177 * A083179 A083180 A083181

Keyword

base,nonn,easy

Author

Amarnath Murthy, Apr 26 2003

Extensions

Corrected and extended by David Wasserman, Oct 25 2004

Status

approved