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 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. 1
 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified September 15 19:46 EDT 2024. Contains 375954 sequences. (Running on oeis4.)