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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
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, 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, 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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,8

COMMENTS

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.

The variant where we drop the condition "i < j" corresponds to A007814. - Rémy Sigrist, Sep 06 2019

LINKS

Aidan Clarke, Table of n, a(n) for n = 1..995

FORMULA

a(n) = 0 iff n belongs to A033627. - Rémy Sigrist, Sep 06 2019

EXAMPLE

a(1) = 0.

a(2) = 0.

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

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

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

MAPLE

for n from 1 to 100 do

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

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

od:

seq(A[i], i=1..100); # Robert Israel, Sep 06 2019

PROG

(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); }

lista(nn) = {my(v = vector(nn)); for (n=1, nn, v[n] = least(v, n); ); v; } \\ Michel Marcus, Sep 07 2019

CROSSREFS

Cf. A007814, A033627.

Sequence in context: A193863 A273496 A286576 * A285193 A213209 A049850

Adjacent sequences:  A322520 A322521 A322522 * A322524 A322525 A322526

KEYWORD

nonn

AUTHOR

Aidan Clarke, Aug 28 2019

STATUS

approved

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Last modified February 20 08:03 EST 2020. Contains 332069 sequences. (Running on oeis4.)