A390294 Numbers k with a prime factor other than 2 or 5 such that digsum(k) = digsum(repeating period of 1/k).

3, 6, 12, 15, 24, 30, 60, 120, 150, 240, 300, 303, 600, 606, 1200, 1500, 1515, 2400, 2424, 3000, 3030, 6000, 6060, 8943, 12000, 13332, 15000, 15150, 19392, 24000, 24240, 30000, 30300, 53328, 54546, 60000, 60600, 76857, 89430, 106656, 120000, 133320, 136365, 150000

Offset

1,1

Comments

If k is in the sequence then so is 10*k. - David A. Corneth, Oct 31 2025

Links

Table of n, a(n) for n=1..44.

Formula

a(n) mod 3 = 0.

Example

3 is a term, because 3 and the repeating period of its reciprocal 3 have both the same digit sum: 3.
6 is a term, because 6 and the repeating period of its reciprocal 6 have both the same digit sum: 6.
606 is a term, because 606 and the repeating period of its reciprocal 0165 have both the same digit sum: 12.
8943 is a term, because 8943 and the repeating period of its reciprocal 0001118193 have both the same digit sum: 24.

Mathematica

q[k_] := Times @@ ({2, 5}^IntegerExponent[k, {2, 5}]) < k && DigitSum[k] == Total[RealDigits[1/k][[1, -1]]]; Select[Range[50000], q] (* Amiram Eldar, Oct 31 2025 *)

Crossrefs

Cf. A003592, A007732, A007953, A070276, A204324, A386682.

Sequence in context: A115803 A290258 A277335 * A267353 A320607 A281063

Adjacent sequences: A390291 A390292 A390293 * A390295 A390296 A390297

Keyword

nonn,base

Author

Jean-Marc Rebert, Oct 31 2025

Extensions

More terms from Amiram Eldar, Oct 31 2025

Status

approved