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

Author

Patrick De Geest, Jan 15 2000

Keywords

• nonn
• base

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.

Examples

			2304 (= 48^2) -> substrings 23, 30, 04, 230, 304 and 2304 are all non-palindromic.
		

Links

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

Crossrefs

Cf. A052061, A052063, A052064, A050749.

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=0,100,if(noPalSub(n^2),print1(n^2", ")))

Formula

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

Extensions

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

Offset changed by Andrew Howroyd, Aug 11 2024