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A284169
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a(n) is the least k such that sigma(binomial(m,k)) = sigma(binomial(m-1,k-1)) + sigma(binomial(m-1,k)) where m = A284168(n).
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1
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1, 2, 5, 5, 9, 3, 17, 13, 21, 10, 18, 6, 28, 32, 33, 26, 20, 27, 28, 19, 12, 41, 34, 42, 54, 25, 5, 28, 84, 22, 40, 5, 54, 44, 56, 25, 29, 86, 81, 89, 88, 134, 10, 71, 148, 69, 87, 27, 91, 92, 18, 128, 23, 51, 52, 153, 108, 202, 112, 138, 58, 201, 141, 162, 176, 77, 4
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OFFSET
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1,2
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COMMENTS
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Consider the triangle formed by replacing each m in Pascal's triangle with sigma(m). Then this sequence consists of the least column indices of the terms that are equal to the sum of its NW and N neighbors, as in a Pascal triangle.
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LINKS
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EXAMPLE
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Here is the triangle also described in A074801.
1,
1, 1,
1, 3, 1,
1, 4, 4, 1,
1, 7, 12, 7, 1,
1, 6, 18, 18, 6, 1,
On row index 3, we have 4 which is the sum of 1 and 3 its NW and N neighbors, this is A284168(1). The corresponding column index is 1, so a(1) = 1.
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PROG
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(PARI) T(n, k) = sigma(binomial(n, k));
isokT(n, k) = T(n-1, k-1) + T (n-1, k) == T(n, k);
isokn(n) = for (k=1, n-1, if (isokT(n, k), return(1)));
listak(nn) = for (n=1, nn, for (k=1, n-1, if (isokT(n, k), print1(k, ", "); break)));
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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