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A089898
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Product of (digits of n each incremented by 1).
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6
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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
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0,2
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COMMENTS
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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.
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LINKS
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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]
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FORMULA
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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
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EXAMPLE
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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.
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MAPLE
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seq(convert(map(`+`, convert(n, base, 10), 1), `*`), n = 0 .. 1000); # Robert Israel, Nov 17 2014
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MATHEMATICA
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a089898[n_Integer] :=
Prepend[Array[Times @@ (IntegerDigits[#] + 1) &, n], 1]; a089898[77] (* Michael De Vlieger, Dec 22 2014 *)
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PROG
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(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
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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