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Search: id:A052062
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| A052062 |
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Squares containing no palindromic substring except single digits. |
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+0
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
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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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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Charles R Greathouse IV, Table of n, a(n) for n=0..10000
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EXAMPLE
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E.g. 2304 (= 48^2) -> substrings 23, 30, 04, 230, 304 and 2304 are all nonpalindromic.
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PROGRAM
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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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Cf. A052061, A052063, A052064, A050749.
Sequence in context: A016073 A115743 A014186 this_sequence A052046 A078255 A077356
Adjacent sequences: A052059 A052060 A052061 this_sequence A052063 A052064 A052065
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KEYWORD
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nonn,base
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AUTHOR
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Patrick De Geest (pdg(AT)worldofnumbers.com), Jan 15 2000.
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EXTENSIONS
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Program and b-file from Charles R Greathouse IV (charles.greathouse(AT)case.edu), Sep 09 2009
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