A052062 Squares containing no palindromic substring except single digits.

0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 169, 196, 256, 289, 324, 361, 529, 576, 625, 729, 784, 841, 961, 1024, 1089, 1296, 1369, 1521, 1681, 1764, 1849, 1936, 2304, 2401, 2601, 2704, 2809, 2916, 3025, 3249, 3481, 3721, 4096, 4356, 4624, 4761, 5041, 5184, 5329

Offset

1,3

Comments

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

A comment in A052061 suggests that this sequence is infinite.

Links

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

Formula

a(n) = A052061(n)^2. - Andrew Howroyd, Aug 11 2024

Example

2304 (= 48^2) -> substrings 23, 30, 04, 230, 304 and 2304 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, 100, if(noPalSub(n^2), print1(n^2", ")))

Crossrefs

Cf. A052061, A052063, A052064, A050749.

Sequence in context: A016073 A115743 A014186 * A052046 A078255 A392242

Adjacent sequences: A052059 A052060 A052061 * A052063 A052064 A052065

Keyword

nonn,base

Author

Patrick De Geest, Jan 15 2000

Extensions

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

Offset changed by Andrew Howroyd, Aug 11 2024

Status

approved