A320121 Numbers k such that the product (m+n)*p, where m,n are the first and the last digits of k, and p is the number which is the part of k between m and n, is a divisor of k.

110, 120, 126, 140, 150, 162, 210, 212, 216, 220, 234, 240, 250, 360, 413, 432, 480, 510, 520, 540, 550, 630, 672, 864, 891, 918, 1010, 1020, 1040, 1050, 1062, 1080, 1100, 1200, 1250, 1400, 1500, 2010, 2012, 2016, 2020, 2034, 2040, 2050, 2072, 2079, 2080, 2100, 2112, 2132, 2176, 2200, 2250, 2400, 2500

Offset: 1

Author

Anton Deynega, Oct 06 2018

Keywords

• nonn
• base

Comments

The sequence is infinite if one considers numbers like 10........010 (with N zeros between ones, N = 0, 1, 2, ...). The problem of looking for odd terms and zerofree terms remains. Still unclear is whether the sequence contains infinitely many zerofree terms. The proportions between numbers of N-digit numbers included in the sequence need to be explored.

Examples

			234 is divisible by 3*(2+4).
1020 is divisible by 2*(1+0).
1062 is divisible by 6*(1+2).
1250 is divisible by 25*(1+0).
		

Crossrefs

Cf. A320292 (zeroless terms).

Programs

Mathematica

Select[Range[100, 2500], Mod[#1, If[#2 == 0, #1 - 1, #2] & @@ {#1, (First@ #2 + Last@ #2) FromDigits@ Most@ Rest@ #2}] == 0 & @@ {#, IntegerDigits@ #} &] (* Michael De Vlieger, Oct 11 2018 *)

PARI

isok(n) = {d = digits(n); if (#d >= 3, x = d[1]; y = d[#d]; w = vector(#d-2, k, d[k+1]); z = fromdigits(w); if (z, return (!(n % (z*(x+y)))));); return (0);} \\ Michel Marcus, Oct 07 2018