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A052062
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Squares containing no palindromic substring except single digits.
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7
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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
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OFFSET
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0,3
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COMMENTS
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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.
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LINKS
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EXAMPLE
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2304 (= 48^2) -> substrings 23, 30, 04, 230, 304 and 2304 are all non-palindromic.
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PROG
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(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}; n=0; for(n=0, 1e4, if(noPalSub(n^2), print1(n^2", ")))
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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