A052064 Cubes containing no palindromic substring except single digits.

0, 1, 8, 27, 64, 125, 216, 512, 729, 1728, 2197, 4096, 4913, 5832, 6859, 9261, 10648, 13824, 15625, 19683, 21952, 24389, 32768, 35937, 42875, 50653, 54872, 59319, 68921, 79507, 85184, 103823, 132651, 185193, 205379, 274625, 287496, 328509

Offset: 1

Author

Patrick De Geest, Jan 15 2000

Keywords

• nonn
• base

Comments

Sequence is probably finite.

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

Examples

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

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1001

Crossrefs

Cf. A052063, A052061, A052062, A050750.

Programs

Mathematica

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 *)

Extensions

Offset changed to 1 by Sean A. Irvine, Oct 17 2019