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Numbers k such that k^3 has an odd number of digits and the middle digit is 9.
12

%I #7 Jan 02 2023 12:30:52

%S 28,33,41,108,132,157,159,175,178,181,184,187,190,193,196,204,207,209,

%T 466,474,480,486,492,508,514,515,518,519,528,536,539,552,570,588,611,

%U 627,638,648,651,657,658,659,660,706,707,708,714,719,745,757,763,765,772

%N Numbers k such that k^3 has an odd number of digits and the middle digit is 9.

%C The sequence of cubes starts: 21952, 35937, 68921, 1259712, 2299968, 3869893, 4019679, 5359375, ...

%H Lars Blomberg, <a href="/A280649/b280649.txt">Table of n, a(n) for n = 1..10000</a>

%H Jeremy Gardiner, <a href="http://list.seqfan.eu/oldermail/seqfan/2016-December/017135.html">Middle digit in cube numbers</a>, Seqfan Mailing list, Dec 12 2016.

%e 28^3 = 21(9)52, 181^3 = 592(9)741, 536^3 = 1539(9)0656.

%t ond9Q[n_]:=Module[{idn=IntegerDigits[n^3],len},len=Length[idn];OddQ[len]&&idn[[(len+1)/2]]==9]; Select[Range[800],ond9Q] (* _Harvey P. Dale_, Mar 14 2018 *)

%Y Cf. A280640-A280648, A181354.

%Y See A279420-A279429 for a k^2 version.

%Y See A279430-A279431 for a k^2 version in base 2.

%K nonn,base,easy

%O 1,1

%A _Lars Blomberg_, Jan 07 2017