A284169 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).

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

Offset

1,2

Comments

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.

Links

Table of n, a(n) for n=1..67.

Example

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.

Prog

(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)));

Crossrefs

Cf. A000203, A007318, A074801, A284168.

Sequence in context: A330447 A145420 A336257 * A152781 A200242 A062553

Adjacent sequences: A284166 A284167 A284168 * A284170 A284171 A284172

Keyword

nonn

Author

Michel Marcus, Mar 21 2017

Status

approved