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 A287336 Numbers k, not ending in 0, such that inserting a 0 between each pair of adjacent digits results in a multiple of k. 1
 1, 2, 3, 4, 5, 6, 7, 8, 9, 15, 18, 45, 111, 126, 222, 285, 333, 444, 555, 666, 777, 888, 999, 1041, 1185, 1395, 1443, 1554, 1665, 1893, 1998, 2082, 2331, 2528, 2757, 2886, 3885, 4662, 4995, 6055, 6993, 7245, 10101, 11111, 11655, 12321, 12987, 13206, 13986 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Sequence is infinite since it contains all the numbers of the form (10^(2*t+1)-1)/9, i.e., repunits with an odd number of digits, like 111, 11111, and so on (A100706). LINKS Giovanni Resta, Table of n, a(n) for n = 1..600 EXAMPLE 41499585 is a term because 401040909050805 is a multiple of 41499585. MAPLE P:=proc(q) local a, k, n; if q mod 10>0 then a:=q; for k from 1 to ilog10(q) do a:=trunc(a/10^(ilog10(a)+2*(1-k)))*10^(ilog10(q)+2-k)+(q mod 10^(ilog10(q)+1-k)); od; if type(a/q, integer) then q; fi; fi; end: seq(P(i), i=1..10^5); # Paolo P. Lava, May 23 2017 MATHEMATICA ins[n_, c_] := Block[{d = IntegerDigits[n]}, FromDigits@ Most@ Flatten@ Transpose[{d, c + 0 Range[Length@d]}]]; Select[Range[10^5], Mod[#, 10] > 0 && Mod[ins[#, 0], #] == 0 &] CROSSREFS Cf. A285176. Sequence in context: A197181 A260352 A049101 * A048406 A081433 A032581 Adjacent sequences: A287333 A287334 A287335 * A287337 A287338 A287339 KEYWORD nonn,base AUTHOR Giovanni Resta, May 23 2017 STATUS approved

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Last modified September 26 02:15 EDT 2023. Contains 365649 sequences. (Running on oeis4.)