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A347943
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Number of ordered pairs (m,k) such that A000009(m) + A000009(k) = n.
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2
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0, 0, 9, 12, 10, 10, 11, 12, 7, 10, 7, 10, 7, 10, 8, 4, 11, 6, 6, 8, 9, 4, 4, 10, 7, 4, 4, 4, 10, 4, 7, 2, 4, 10, 6, 4, 3, 6, 2, 8, 8, 2, 6, 2, 5, 2, 2, 8, 6, 4, 6, 2, 2, 2, 5, 6, 8, 2, 4, 4, 4, 2, 2, 0, 5, 8, 6, 2, 4, 4, 4, 0, 4, 2, 2, 0, 5, 6, 6, 4, 2, 4, 4, 0, 4, 0, 6, 0, 2, 0
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OFFSET
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0,3
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COMMENTS
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Although a(n) != 0 for 2 <= n <= 62, it seems that most terms are zero. There are only 1351 nonzero terms among a(0) through a(10000).
a(n) is odd if and only if n != 4 and n/2 is in A000009.
Conjecture: a(n) = 0, 1, 2, 4, 6 for all n > 29696.
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LINKS
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FORMULA
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a(1+A000009(m)) >= 6. It seems that for n > 24578, all terms with a(n) >= 6 are of the form 1 + A000009(m), and in which case we have a(n) = 6.
a(2+A000009(m)) >= 4. It seems that for n > 729124, all terms with a(n) = 4 are of the form 2 + A000009(m).
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EXAMPLE
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a(6) = 11 since 6 = A000009(m) + A000009(k) for (m,k) = (0,7), (1,7), (2,7), (3,6), (4,6), (5,5), (6,3), (6,4), (7,0), (7,1), (7,2).
a(63) = 0 since no two terms in A000009 sum up to 63.
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MATHEMATICA
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Table[Length@Select[Tuples[k=1; While[Max[p=PartitionsQ/@Range[0, k++]]<n]; Most@p, {2}], Total@#==n&], {n, 0, 100}] (* Giorgos Kalogeropoulos, Sep 21 2021 *)
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PROG
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v(n) = my(l=leng(n), v=[]); for(i=0, l-1, v=concat(v, vector(l, j, A000009(i)+A000009(j-1)))); v=vecsort(v); v
list(n) = my(v=v(n), w=vector(n), size=#v); for(i=1, size, if(v[i]<=n, w[v[i]]++, break())); w=concat([0], w); w
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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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