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A328882
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a(n) = n - 2^(sum of digits of n).
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5
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-1, -1, -2, -5, -12, -27, -58, -121, -248, -503, 8, 7, 4, -3, -18, -49, -112, -239, -494, -1005, 16, 13, 6, -9, -40, -103, -230, -485, -996, -2019, 22, 15, 0, -31, -94, -221, -476, -987, -2010, -4057, 24, 9, -22, -85, -212, -467, -978, -2001, -4048, -8143, 18, -13, -76, -203, -458, -969, -1992, -4039, -8134, -16325, -4
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OFFSET
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0,3
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COMMENTS
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This sequence is a map from the set of nonnegative integers into the set of all integers. It is clearly not one-to-one. It is not known if it is onto.
For m >= 0, A329002 gives an expression for the first time that m appears in this sequence (if it does appear), and A329492 plays a similar role for negative m.
In all these sequences it is safer to say "sum of digits" (which is A007953) rather than "digital sum" (which is also A007953), because many people confuse the latter term with the "digital root" (A010888). (End)
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LINKS
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FORMULA
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EXAMPLE
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a(0) = 0 - 2^0 = -1.
a(11) = 11 - 2^(1+1) = 7.
a(32) = 32 - 2^(3+2) = 0. The next time 0 occurs is at a(1180591620717411303424) = 1180591620717411303424 - 2^(70)=0.
The only known occurrence of 1 is when n=513: a(513) = 513 - 2^(5+1+3) = 1.
k = 0 1 2 3 4 5 6 7 8 9 10 ...
n = 32 513 2^103+2 1027 12 133 22 11 10 41 522 ...
k = -1 -2 -3 -4 -5 -6 -7 -8 -9 -10 11 ...
n = 0 2 13 60 3 1018 2^103-7 504 23 2^18-10 ? ...
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MATHEMATICA
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PROG
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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