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A307707
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Lexicographically earliest sequence starting with a(1) = 0 such that a(n) is the number of pairs of contiguous terms whose sum is a(n).
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2
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0, 1, 1, 1, 2, 1, 2, 2, 2, 2, 2, 3, 2, 3, 2, 3, 3, 3, 3, 3, 3, 3, 4, 3, 4, 3, 4, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 5, 6, 5, 6, 5, 6, 5, 6, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 6, 7, 6, 7, 6, 7, 6, 7, 6, 7, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8
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OFFSET
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1,5
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COMMENTS
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In order to avoid the trivial case "0 followed by 1's", the sum of every pair of consecutive terms must appear in the sequence. - Rémy Sigrist, Apr 24 2019
From Paul Curtz, Apr 27 2019: This can be written as a triangle:
0
1 1
1 2 1
2 2 2 2
2 3 2 3 2
3 3 3 3 3 3
3 4 3 4 3 4 3
...
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LINKS
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FORMULA
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EXAMPLE
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The sequence starts with 0,1,1,1,2,1,2,2,2,2,2,3,2,3,2...
a(1) = 0 means that the sum [a(n) + a(n+1)] is never = 0;
a(2) = 1 means that the sum [a(n) + a(n+1)] = 1 is true only once [this is the sum a(1) + a(2) = 0 + 1 = 1] ;
...
a(5) = 2 means that the sum [a(n) + a(n+1)] = 2 is true only twice [those are the sums a(2) + a(3) = 1 + 1 = 2 and a(3) + a(4) = 1 + 1 = 2];
...
a(12) = 3 means that the sum [a(n) + a(n+1)] = 3 is true only three times [those are the three sums a(4) + a(5) = 1 + 2 = 3; a(5) + a(6) = 2 + 1 = 3 and a(6) + a(7) = 1 + 2 = 3]; etc.
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MATHEMATICA
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m = 107; a[1]=0;
a24[n_] := Ceiling[(Sqrt[8n+1]-1)/2];
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PROG
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(PARI) v=0; rem=wanted=1; for (n=1, 107, print1 (v", "); v=wanted-v; if (rem--==0, rem=wanted++)) \\ Rémy Sigrist, Apr 23 2019
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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