A320292 Zerofree 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.

126, 162, 212, 216, 234, 413, 432, 672, 864, 891, 918, 2112, 2132, 2176, 2691, 2772, 2871, 2912, 3168, 4144, 4199, 4224, 4455, 5184, 6336, 8448, 21372, 21771, 23391, 43673, 53768, 55328, 64116, 171432, 228177, 316764, 412272, 515484, 594342, 638715, 663832, 824544, 1588248, 5136248, 7222932

Offset: 1

Author

Anton Deynega, Oct 09 2018

Keywords

• nonn
• base

Comments

This sequence is infinite since it contains all the terms of the form 6*(10^(6*t)+20)/35 and 33*(10^(6*t)*75+2)/7 for t > 0. The first pattern corresponds to terms 171432, 171428571432, 171428571428571432, ..., the second to terms 353571438, 353571428571438, 353571428571428571438,... . - Giovanni Resta, Oct 10 2018

Examples

			234 is divisible by 3*(2+4).
4199 is divisible by 19*(4+9).
7222932 is divisible by 22293*(7+2).
		

Crossrefs

Intersection of A052382 and A320121.

Programs

Mathematica

Select[Range[100, 10^6], And[FreeQ[#2, 0], 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) && vecmin(d), 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 10 2018