cp's OEIS Frontend

A267085 Numbers such that the number formed by digits in even position divides, or is divisible by, the number formed by the digits in odd position; both must be nonzero.

%I A267085 #16 Dec 23 2024 14:53:44
%S A267085 11,12,13,14,15,16,17,18,19,21,22,24,26,28,31,33,36,39,41,42,44,48,51,
%T A267085 55,61,62,63,66,71,77,81,82,84,88,91,93,99,110,111,112,113,114,115,
%U A267085 116,117,118,119,120,122,124,126,128,132,135,138,142,146,150,155,162,168,174,186,198
%N A267085 Numbers such that the number formed by digits in even position divides, or is divisible by, the number formed by the digits in odd position; both must be nonzero.
%C A267085 Termed "integears" by Eric Angelini. See A267086 for the "extended version" where zero is allowed.
%H A267085 Michael De Vlieger, <a href="/A267085/b267085.txt">Table of n, a(n) for n = 1..10000</a>
%H A267085 E. Angelini, <a href="https://web.archive.org/web/*/http://list.seqfan.eu/oldermail/seqfan/2016-January/015951.html">Integears</a>, SeqFan list, Jan. 10, 2016.
%t A267085 Select[Range[10, 200], Or[If[#2 == 0, False, Mod[#1, #2] == 0], If[#2 == 0, False, Mod[#2, #1] == 0]] & @@ {FromDigits@ Extract[#, Range[1, Length@ #, 2] /. x_Integer -> {x}], FromDigits@ Extract[#, Range[2, Length@#, 2] /. x_Integer -> {x}]} &@ IntegerDigits@ # &] (* _Michael De Vlieger_, Jan 21 2016 *)
%o A267085 (PARI) is(n,d=digits(n))={n=d*matrix(#d,2,z,s,if(z==Mod(s,2),10^((#d-z)\2))); n[2] && (n[1]%n[2]==0 || n[2]%n[1]==0)}
%Y A267085 See also A080463, A080464 and A080465.
%K A267085 nonn,base
%O A267085 1,1
%A A267085 _Eric Angelini_ and _M. F. Hasler_, Jan 10 2016