cp's OEIS Frontend

A249722 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.

%I A249722 #13 Nov 05 2014 11:24:03
%S A249722 4,6,8,12,14,16,17,20,22,24,25,26,28,30,32,33,34,35,38,40,41,42,44,48,
%T A249722 49,50,51,52,53,56,57,58,60,61,62,64,65,66,67,68,69,70,71,74,76,77,78,
%U A249722 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
%N A249722 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.
%C A249722 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.
%H A249722 Antti Karttunen, <a href="/A249722/b249722.txt">Table of n, a(n) for n = 1..10000</a>
%e A249722 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.
%e A249722 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.
%o A249722 (PARI)
%o A249722 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++); }
%Y A249722 A subsequence of A249724.
%Y A249722 Natural numbers (A000027) is a disjoint union of the sequences A048278, A249722, A249723 and A249726.
%Y A249722 Cf. A007318, A034931, A095143, A048645, A051382.
%K A249722 nonn
%O A249722 1,1
%A A249722 _Antti Karttunen_, Nov 04 2014