A052061 Numbers k such that decimal expansion of k^2 contains no palindromic substring except single digits.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 13, 14, 16, 17, 18, 19, 23, 24, 25, 27, 28, 29, 31, 32, 33, 36, 37, 39, 41, 42, 43, 44, 48, 49, 51, 52, 53, 54, 55, 57, 59, 61, 64, 66, 68, 69, 71, 72, 73, 74, 75, 78, 79, 82, 84, 86, 87, 89, 93, 95, 96, 97, 98, 99, 104, 113, 116, 117, 118, 124

Offset: 1

Author

Patrick De Geest, Jan 15 2000

Keywords

• nonn
• base

Comments

Leading zeros in the substrings are allowed so 103^2 = 10609 is rejected because 1{060}9 contains a palindromic substring.

Probabilistic analysis strongly suggests that this sequence is not finite. - Franklin T. Adams-Watters, Nov 15 2006

Examples

			118^2 = 13924 -> substrings 13, 39, 92, 24, 139, 392, 924, 1392, 3924 and 13924 are all non-palindromic.
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10001

Crossrefs

Cf. A052062, A052063, A052064, A050741.

Programs

PARI

noPalSub(n)={my(d);local(digit);digit=eval(Vec(Str(n)));d = #digit;for(len=2,d,for(i=1,d-len+1,if(isPalSub(i,len), return(0))));1};
isPalSub(start,len)={my(b=start-1,e=start+len);for(j=1,len>>1,if(digit[b+j] != digit[e-j], return(0)));1};
for(n=0,200,if(noPalSub(n^2),print1(n", ")))

Extensions

Program and b-file from Charles R Greathouse IV, Sep 09 2009