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A329725
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a(1)=0, a(n) = n - (product of nonzero digits of n) - a(n-1).
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1
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0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 1, 9, 1, 9, 1, 9, 1, 9, 1, 17, 2, 16, 1, 15, 0, 14, -1, 13, -2, 29, -1, 27, -3, 25, -5, 23, -7, 21, -9, 45, -8, 42, -11, 39, -14, 36, -17, 33, -20, 65, -19, 61, -23, 57, -27, 53, -31, 49, -35, 89, -34, 84, -39, 79, -44, 74, -49, 69, -54, 117
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OFFSET
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1,10
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COMMENTS
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a(10n+1)-a(10n-1)=1 for all positive integer n (conjectured).
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LINKS
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FORMULA
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EXAMPLE
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a(22) = 22 - 2*2 - 2 = 16.
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MAPLE
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R:= ListTools:-PartialSums(map(n -> (-1)^n*(n - convert(subs(0=NULL, convert(n, base, 10)), `*`)), [$1..100])):
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MATHEMATICA
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Nest[Append[#1, #2 - Last[#1] - Times @@ DeleteCases[IntegerDigits[#2], 0]] & @@ {#, Length@ # + 1} &, {0}, 69] (* Michael De Vlieger, Nov 19 2019 *)
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PROG
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(PARI) for (n=1, 70, print1 (v=if (n==1, 0, n - vecprod(select(sign, digits(n))) - v)", ")) \\ Rémy Sigrist, Nov 28 2019
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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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