A089898 - OEIS

A089898

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

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)/(x-1)^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

(PARI) a(n) = vecprod(apply(x->x+1, digits(n))); \\ Michel Marcus, Feb 01 2023

(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