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

Author

Amarnath Murthy, Apr 26 2003

Keywords

• base
• nonn
• easy

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

Crossrefs

Cf. A000792.

Programs

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

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

Extensions

Corrected and extended by David Wasserman, Oct 25 2004