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Cubes containing no palindromic substring except single digits.
6

%I #16 Oct 18 2019 04:00:50

%S 0,1,8,27,64,125,216,512,729,1728,2197,4096,4913,5832,6859,9261,10648,

%T 13824,15625,19683,21952,24389,32768,35937,42875,50653,54872,59319,

%U 68921,79507,85184,103823,132651,185193,205379,274625,287496,328509

%N Cubes containing no palindromic substring except single digits.

%C Sequence is probably finite.

%C Leading zeros in substring allowed so 52^2 = 140608 is rejected because 14{060}8 contains a palindromic substring.

%H Harvey P. Dale, <a href="/A052064/b052064.txt">Table of n, a(n) for n = 1..1001</a>

%e 132651 (= 51^3) -> substrings 13, 32, 26, 65, 51, 132, 326, 265, 651, 1326, 3265, 2651, 13265, 32651 and 132651 are all non-palindromic.

%t npsQ[n_]:=Count[Flatten[Table[Partition[IntegerDigits[n],i,1],{i,2, IntegerLength[ n]}],1],_?(#==Reverse[#]&)]==0; Select[Range[ 0,100]^3, npsQ] (* _Harvey P. Dale_, Dec 10 2016 *)

%Y Cf. A052063, A052061, A052062, A050750.

%K nonn,base

%O 1,3

%A _Patrick De Geest_, Jan 15 2000

%E Offset changed to 1 by _Sean A. Irvine_, Oct 17 2019