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A033627
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0-additive sequence: not the sum of any previous pair.
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35
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1, 2, 4, 7, 10, 13, 16, 19, 22, 25, 28, 31, 34, 37, 40, 43, 46, 49, 52, 55, 58, 61, 64, 67, 70, 73, 76, 79, 82, 85, 88, 91, 94, 97, 100, 103, 106, 109, 112, 115, 118, 121, 124, 127, 130, 133, 136, 139, 142, 145, 148, 151, 154, 157, 160, 163, 166, 169, 172, 175
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OFFSET
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1,2
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COMMENTS
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Conjecture: a(n+1) is the number of distinct numbers of steps required for the last n digits of integers to repeat themselves by iterating the map m -> m^2 + 1. - Ya-Ping Lu, Oct 19 2021
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REFERENCES
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R. K. Guy, Unsolved Problems in Number Theory, C4
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LINKS
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FORMULA
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2 together with numbers of form 3k+1.
Equals binomial transform of [1, 1, 1, 0, -1, 2, -3, 4, -5, 6, -7, ...].
Equals sum of antidiagonal terms of the following arithmetic array: 1, 1, 1, 1, 1, ... 1, 2, 3, 4, 5, ... 1, 3, 5, 7, 9, ... . (End)
a(n) = 3*n - 5, for n > 2.
a(n) = 2*a(n-1) - a(n-2), for n > 4;
G.f.: x*(1+x^2+x^3)/(1-x)^2. (End)
E.g.f.: 5 + 3*x + x^2/2 + exp(x)*(3*x - 5). - Stefano Spezia, Apr 15 2023
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MATHEMATICA
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f[s_List] := Block[{k = s[[-1]] + 1, ss = Union[ Plus @@@ Subsets[s, {2}]]}, While[ MemberQ[ ss, k], k++]; Append[ s, k]]; Nest[f, {1}, 70] (* Robert G. Wilson v, Jun 23 2014 *)
CoefficientList[Series[x(1+x^2+x^3)/(1-x)^2 , {x, 0, 70}], x] (* Stefano Spezia, Oct 04 2018 *)
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PROG
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(Haskell)
import Data.List ((\\))
a033627 n = a033627_list !! (n-1)
a033627_list = f [1..] [] where
f (x:xs) ys = x : f (xs \\ (map (+ x) ys)) (x:ys)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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