login
A284168
Integers n such that sigma(binomial(n,k)) = sigma(binomial(n-1,k-1)) + sigma(binomial(n-1,k)) for some k.
1
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.
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
KEYWORD
nonn
AUTHOR
Michel Marcus, Mar 21 2017
STATUS
approved