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A249722
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Numbers n such that there is 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.
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5
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4, 6, 8, 12, 14, 16, 17, 20, 22, 24, 25, 26, 28, 30, 32, 33, 34, 35, 38, 40, 41, 42, 44, 48, 49, 50, 51, 52, 53, 56, 57, 58, 60, 61, 62, 64, 65, 66, 67, 68, 69, 70, 71, 74, 76, 77, 78, 80, 84, 86, 88, 89, 92, 94, 96, 97, 98, 100, 101, 102, 104, 105, 106, 107, 112, 113, 114, 115, 116, 120, 121, 122, 124, 125
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,1
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COMMENTS
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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 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 latter triangle.
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LINKS
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EXAMPLE
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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.
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PROG
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(PARI)
A249722list(upto_n) = { my(i=0, n=0); while(i<upto_n, for(k=0, n\2, if(!(binomial(n, k)%9), break, if(!(binomial(n, k)%4), i++; write("b249722.txt", i, " ", n); break))); n++); }
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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