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 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. 1
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 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 LINKS EXAMPLE 234 is divisible by 3*(2+4). 4199 is divisible by 19*(4+9). 7222932 is divisible by 22293*(7+2). 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 *) PROG (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 CROSSREFS Intersection of A052382 and A320121. Sequence in context: A179482 A009944 A203566 * A104395 A267331 A267739 Adjacent sequences:  A320289 A320290 A320291 * A320293 A320294 A320295 KEYWORD nonn,base AUTHOR Anton Deynega, Oct 09 2018 STATUS approved

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Last modified May 19 05:04 EDT 2022. Contains 353826 sequences. (Running on oeis4.)