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

1,1

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.

Links

Table of n, a(n) for n=1..55.

Example

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).

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 *)

Prog

(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

Crossrefs

Cf. A320292 (zeroless terms).

Sequence in context: A135642 A166323 A194429 * A084042 A110735 A277622

Adjacent sequences: A320118 A320119 A320120 * A320122 A320123 A320124

Keyword

nonn,base

Author

Anton Deynega, Oct 06 2018

Status

approved