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

1,3

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

Links

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

Example

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

Prog

(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", ")))

Crossrefs

Cf. A052062, A052063, A052064, A050741.

Sequence in context: A305932 A213882 A135140 * A045540 A119509 A219248

Adjacent sequences: A052058 A052059 A052060 * A052062 A052063 A052064

Keyword

nonn,base

Author

Patrick De Geest, Jan 15 2000

Extensions

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

Status

approved