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A249723 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.

%I A249723 #17 Nov 05 2014 11:25:33
%S A249723 9,10,13,15,18,19,21,27,29,31,37,39,43,45,46,47,54,55,59,63,75,79,81,
%T A249723 82,83,85,87,90,91,93,95,99,103,109,111,117,118,119,123,126,127,135,
%U A249723 139,151,153,154,157,159,162,163,165,167,171,175,181,183,187,189,190,191,198,199,207,219,223,225,226,229,231,234,235,237,239,243,245,247,251,253,255
%N A249723 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.
%C A249723 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.
%C A249723 A052955 from its eight term onward, 31, 47, 63, 95, 127, ... seems to be a subsequence. See also the comments at A249441.
%H A249723 Antti Karttunen, <a href="/A249723/b249723.txt">Table of n, a(n) for n = 1..10000</a>
%e A249723 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.
%o A249723 (PARI)
%o A249723 A249723list(upto_n) = { my(i=0, n=0); while(i<upto_n,for(k=0,n\2, if(!(binomial(n,k)%4), break, if(!(binomial(n,k)%9), i++;write("b249723.txt",i," ",n);break))); n++); }
%Y A249723 Complement: A249724.
%Y A249723 Natural numbers (A000027) is a disjoint union of the sequences A048278, A249722, A249723 and A249726.
%Y A249723 Cf. A007318, A034931, A048645, A051382, A095143, A052955, A249441, A249695.
%Y A249723 Cf. A048278, A249722, A249726, A249731, A249732, A249733.
%K A249723 nonn
%O A249723 1,1
%A A249723 _Antti Karttunen_, Nov 04 2014