A284168 Integers n such that sigma(binomial(n,k)) = sigma(binomial(n-1,k-1)) + sigma(binomial(n-1,k)) for some k.

3, 6, 15, 25, 27, 30, 35, 40, 48, 50, 54, 60, 63, 66, 78, 80, 100, 108, 112, 118, 120, 123, 124, 126, 140, 144, 158, 175, 192, 198, 200, 207, 216, 220, 224, 225, 232, 238, 243, 247, 304, 310, 316, 319, 341, 345, 348, 358, 364, 368, 375, 385, 391, 408, 416, 425, 432

Offset

1,1

Comments

Consider the triangle formed by replacing each m in Pascal's triangle with sigma(m). Then this sequence consists of the row indices where there is a term that is equal to the sum of its NW and N neighbors as in a Pascal triangle.

Links

Table of n, a(n) for n=1..57.

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.
So a(1)= 3, and its column index is 1 which will be corresponding value in A284169.

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)));

Crossrefs

Cf. A000203, A007318, A074801, A284169.

Sequence in context: A286502 A287101 A287189 * A216304 A020991 A079825

Adjacent sequences: A284165 A284166 A284167 * A284169 A284170 A284171

Keyword

nonn

Author

Michel Marcus, Mar 21 2017

Status

approved