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A322523 a(n) is the least nonnegative integer k for which there does not exist i < j with i+j=n and a(i)=a(j)=k. 1


%S 0,0,1,0,1,1,0,2,2,0,2,1,0,1,2,0,3,2,0,3,1,0,1,3,0,3,3,0,3,1,0,1,3,0,

%T 2,2,0,2,1,0,1,2,0,4,3,0,4,1,0,1,4,0,4,3,0,4,1,0,1,4,0,2,2,0,2,1,0,1,

%U 2,0,4,4,0,4,1,0,1,4,0,4,4,0,4,1,0,1,4,0,2,2,0,2,1,0,1,2,0,3,4,0

%N a(n) is the least nonnegative integer k for which there does not exist i < j with i+j=n and a(i)=a(j)=k.

%C If x is an integer that we are checking whether it is an option for a(n), at position n = 3(3^(x+1)-1)/2 there appears to begin a repeating sequence (containing 3^(x+1) terms) of whether it can or cannot be used for a(n) that continues infinitely.

%C The variant where we drop the condition "i < j" corresponds to A007814. - _Rémy Sigrist_, Sep 06 2019

%H Aidan Clarke, <a href="/A322523/b322523.txt">Table of n, a(n) for n = 1..995</a>

%F a(n) = 0 iff n belongs to A033627. - _Rémy Sigrist_, Sep 06 2019

%e a(1) = 0.

%e a(2) = 0.

%e a(3) = 1 (because a(1) and a(2) both equal 0).

%e a(5) = 1 (because a(1) and a(4) both equal 0).

%e a(8) = 2 (because a(1) and a(7) equal 0, and a(3) and a(5) equal 1).

%p for n from 1 to 100 do

%p forbid:= {seq(A[i],i= select(i -> A[i]=A[n-i],[$1..(n-1)/2]))};

%p if forbid = {} then A[n]:= 0 else A[n]:= min({$0..max(forbid)+1} minus forbid) fi;

%p od:

%p seq(A[i],i=1..100); # _Robert Israel_, Sep 06 2019

%o (PARI) least(v, n) = {my(found = []); for (i=1, n, if (i >= n-i, break, if (v[i] == v[n-i], found = Set(concat(found, v[i]))));); if (#found == 0, return(0)); my(m = vecmax(found)); for (i=0, m, if (!vecsearch(found, i), return (i))); return (m+1);}

%o lista(nn) = {my(v = vector(nn)); for (n=1, nn, v[n] = least(v, n);); v;} \\ _Michel Marcus_, Sep 07 2019

%Y Cf. A007814, A033627.

%K nonn

%O 1,8

%A _Aidan Clarke_, Aug 28 2019

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Last modified April 3 01:23 EDT 2020. Contains 333195 sequences. (Running on oeis4.)