STATUS
editing
approved
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Revision History for A249723
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Numbers n such that there is a multiple of 9 on row n of Pascal's triangle with property that all multiples of 4 on the same row (if they exist) are larger than it.
(history; published version)
(history; published version)
NAME
Numbers n such that there is such a multiple of 9 on row n of Pascal's triangle with property that all multiples of 4 on the same row (if they exist) are larger than it.
STATUS
proposed
editing
STATUS
editing
proposed
EXAMPLE
Row 13 of Pascal's triangle (A007318) is: {1, 13, 78, 286, 715, 1287, 1716, 1716, 1287, 715, 286, 78, 13, 1} and the term binomial(13, 5) = 1287 = 9*11*13 occurs before any term which is a multiple of 4. Note that one such term occurs right next to it, as binomial(13, 6) = 1716 = 4*3*11*13, but 1287 < 1716, thus 13 is included.
{1, 13, 78, 286, 715, 1287, 1716, 1716, 1287, 715, 286, 78, 13, 1}
and the term binomial(13, 5) = 1287 = 9*11*13 occurs before any term which is a multiple of 4. Note that one such term occurs right next to it, as binomial(13, 6) = 1716 = 4*3*11*13, but 1287 < 1716, thus 13 is included.
NAME
Numbers n such that there is such a multiple of 9 on row n of Pascal's triangle that all multiples of 4 on the same row there (if they exist) are no multiple of 4 which would be less larger than or equal to it.
NAME
Numbers n such that there is such a term divisible by multiple of 9 on row n of Pascal's triangle and that on the same row there are no terms multiple of 4 which would be less than or equal to that which were divisible by 4it.
COMMENTS
All n such that on row n of A095143 (Pascal's triangle reduced modulo 9) there is at least one zero and the distance from the edge to the nearest zero is shorter than the distance from the edge to the nearest zero on row n of A034931 (Pascal's triangle reduced modulo 4), the latter distance taken to be infinite if there are no zeros on that row in the latter triangle.
COMMENTS
All n such that on row n of A095143 (Pascal's triangle reduced modulo 9) there is a at least one zero nearer to and the distance from the edge to the nearest zero is shorter than the distance from the edge to the nearest zero on row n of A034931 (Pascal's triangle reduced modulo 4), the latter taken to be infinite if there are no zeros on that row in the latter triangle.