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

1,3

Comments

Sequence is probably finite.

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

Links

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

Example

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

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 *)

Crossrefs

Cf. A052063, A052061, A052062, A050750.

Sequence in context: A100571 A125084 A052048 * A352049 A125496 A030289

Adjacent sequences: A052061 A052062 A052063 * A052065 A052066 A052067

Keyword

nonn,base

Author

Patrick De Geest, Jan 15 2000

Extensions

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

Status

approved