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A083178
Numbers with a digit sum of n and a maximum product of digits. In case of two identical products choose the largest number.
2
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
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
KEYWORD
base,nonn,easy
AUTHOR
Amarnath Murthy, Apr 26 2003
EXTENSIONS
Corrected and extended by David Wasserman, Oct 25 2004
STATUS
approved