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.

11, 12, 13, 14, 15, 16, 17, 18, 19, 21, 22, 24, 26, 28, 31, 33, 36, 39, 41, 42, 44, 48, 51, 55, 61, 62, 63, 66, 71, 77, 81, 82, 84, 88, 91, 93, 99, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 122, 124, 126, 128, 132, 135, 138, 142, 146, 150, 155, 162, 168, 174, 186, 198

Offset: 1

Author

Eric Angelini and M. F. Hasler, Jan 10 2016

Keywords

• nonn
• base

Comments

Termed "integears" by Eric Angelini. See A267086 for the "extended version" where zero is allowed.

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..10000
• E. Angelini, Integears, SeqFan list, Jan. 10, 2016.

Crossrefs

See also A080463, A080464 and A080465.

Programs

Mathematica

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 *)

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)}