editing

approved

Numbers n such that there is such a multiple of 4 on row n of Pascal's triangle with property that all multiples of 9 on the same row (if they exist) are larger than it.

proposed

editing

editing

proposed

Natural numbers A000027 All n such that on row n of A034931 (Pascal's triangle reduced modulo 4) there is at least one zero and the distance from the edge to the nearest zero is a disjoint union shorter than the distance from the edge to the nearest zero on row n of A095143 (Pascal's triangle reduced modulo 9), the latter distance taken to be infinite if there are no zeros on that row in the sequences A048278, A249722, A249723, A249726latter triangle.

Row 4 of Pascal's triangle (A007318) is {1,4,6,4,1}. The least multiple of 4 occurs as C(4,1) = 4, and there are no multiples of 9 present, thus 4 is included among the terms.

Row 12 of Pascal's triangle is {1,12,66,220,495,792,924,792,495,220,66,12,1}. The least multiple of 4 occurs as C(12,1) = 12, which is less than the least multiple of 9 present at C(12,4) = 495 = 9*55, thus 12 is included among the terms.

Cf. Natural numbers (A000027) is a disjoint union of the sequences A048278, A249722, A249723, and A249726, A048645, A051382.

Cf. A007318, A034931, A095143, A048645, A051382.

Row 4 of Pascal's triangle is {1,4,6,4,1}. The first least multiple of 4 occurs as C(4,1) = 4, and there are no multiples of 9 present, thus 4 is included among the terms.

Row 6 12 of Pascal's triangle is {1,6,15,20,15,6,12,66,220,495,792,924,792,495,220,66,12,1}. The first least multiple of 4 occurs as C(6,312,1) = 20, and there are no multiples 12, which is less than the least multiple of 9 present, at C(12,4) = 495 = 9*55, thus 6 12 is included among the terms.

Row 12 of Pascal's triangle is {1,12,66,220,495,792,924,792,495,220,66,12,1}. The first multiple of 4 is C(12,1) = 12, which is less than the first multiple of 9 at C(12,4) = 495 = 9*55, thus 12 is included among the terms.

Row 4 of Pascal's triangle is {1,4,6,4,1}. The first multiple of 4 occurs as C(4,1) = 4, and there are no multiples of 9 present, thus 4 is included among the terms.

Row 6 of Pascal's triangle is {1,6,15,20,15,6,1}. The first multiple of 4 occurs as C(6,3) = 20, and there are no multiples of 9 present, thus 6 is included among the terms.

Row 12 of Pascal's triangle is {1,12,66,220,495,792,924,792,495,220,66,12,1}. The first multiple of 4 is C(12,1) = 12, which is less than the first multiple of 9 at C(12,4) = 495 = 9*55, thus 12 is included among the terms.

Cf. A048278, A249723, A249726, A048645, A051382.

Numbers n such that there is such a term divisible by multiple of 4 on row n of Pascal's triangle and there are no lesser or equal terms divisible by that all multiples of 9 on the same row (if they exist) are larger than it.

A subsequence of A249724.

Natural numbers A000027 is a disjoint union of the sequences A048278, A249722, A249723, A249726.