A052063 - OEIS

%I #20 May 13 2022 10:10:04

%S 0,1,2,3,4,5,6,8,9,12,13,16,17,18,19,21,22,24,25,27,28,29,32,33,35,37,

%T 38,39,41,43,44,47,51,57,59,65,66,69,73,75,76,84,88,93,94,97,102,108,

%U 109,115,116,123,125,128,133,134,135,139,144,145,147,148,155,156,159

%N Numbers k such that the decimal expansion of k^3 contains no palindromic substring except single digits.

%C Leading zeros in substring are allowed so 52^3 = 140608 is rejected because 14{060}8 contains a palindromic substring.

%C Probabilistic analysis strongly suggests that this sequence is not finite. - _Franklin T. Adams-Watters_, Nov 15 2006

%H Michael S. Branicky, <a href="/A052063/b052063.txt">Table of n, a(n) for n = 1..10000</a>

%e 19^3 = 6859 -> substrings 68, 85, 59, 685, 859 and 6859 are all non-palindromic.

%t testQ@l_ :=

%t NoneTrue[Flatten[Table[Partition[l, n, 1], {n, 2, Length@l}], 1],

%t   PalindromeQ];

%t f@nn_ := Select[Range@nn, testQ@IntegerDigits@(#^3) &]; f[300]

%t (* _Hans Rudolf Widmer_, May 13 2022 *)

%o (Python)

%o def nopal(s): return all(ss != ss[::-1] for ss in (s[i:j] for i in range(len(s)-1) for j in range(i+2, len(s)+1)))

%o def ok(n): return nopal(str(n**3))

%o print([k for k in range(160) if ok(k)]) # _Michael S. Branicky_, May 13 2022

%Y Cf. A052064, A052061, A052062, A050742.

%K nonn,base

%O 1,3

%A _Patrick De Geest_, Jan 15 2000