

A089898


Product of (digits of n each incremented by 1).


4



1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 8, 16, 24, 32, 40, 48, 56, 64
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OFFSET

0,2


COMMENTS

Sum of products of all subsets of digits of n (with the empty subset contributing 1).
Number of nonnegative values k such that the lunar sum of k and n is n.
First 100 values are 10 X 10 multiplication table, read by rows/columns.


LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000
D. Applegate, M. LeBrun and N. J. A. Sloane, Dismal Arithmetic, arXiv:1107.1130 [math.NT], 2011. [Note: we have now changed the name from "dismal arithmetic" to "lunar arithmetic"  the old name was too depressing]


FORMULA

a(n) = a(floor(n/10))*(1+(n mod 10)).  Robert Israel, Nov 17 2014
G.f. g(x) satisfies g(x) = (10*x^11  11*x^10 + 1)*g(x^10)/(x1)^2.  Robert Israel, Nov 17 2014


EXAMPLE

a(12)=6 since (1+1)*(2+1)=2*3=6 and since (1*2)+(1)+(2)+(1)=2+1+2+1=6 and since the lunar sum of 12 with any of the six values {0,1,2,10,11,12} is 12.


MAPLE

seq(convert(map(`+`, convert(n, base, 10), 1), `*`), n = 0 .. 1000); # Robert Israel, Nov 17 2014


MATHEMATICA

a089898[n_Integer] :=
Prepend[Array[Times @@ (IntegerDigits[#] + 1) &, n], 1]; a089898[77] (* Michael De Vlieger, Dec 22 2014 *)


PROG

(PARI) a(n) = my(d=digits(n)); prod(i=1, #d, d[i]+1); \\ Michel Marcus, Apr 06 2014
(Haskell)
a089898 n = if n < 10 then n + 1 else (d + 1) * a089898 n'
where (n', d) = divMod n 10
 Reinhard Zumkeller, Jul 06 2014


CROSSREFS

Cf. A007954, A087061, A001316, A006047.
Sequence in context: A053392 A114925 A043270 * A071785 A079050 A320109
Adjacent sequences: A089895 A089896 A089897 * A089899 A089900 A089901


KEYWORD

base,easy,nonn,look


AUTHOR

Marc LeBrun, Nov 13 2003


STATUS

approved



