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%I #23 Oct 18 2019 21:24:18
%S 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,
%T 37,39,41,42,43,44,48,49,51,52,53,54,55,57,59,61,64,66,68,69,71,72,73,
%U 74,75,78,79,82,84,86,87,89,93,95,96,97,98,99,104,113,116,117,118,124
%N Numbers k such that decimal expansion of k^2 contains no palindromic substring except single digits.
%C Leading zeros in the substrings are allowed so 103^2 = 10609 is rejected because 1{060}9 contains a palindromic substring.
%C Probabilistic analysis strongly suggests that this sequence is not finite. - _Franklin T. Adams-Watters_, Nov 15 2006
%H Charles R Greathouse IV, <a href="/A052061/b052061.txt">Table of n, a(n) for n = 1..10001</a>
%e 118^2 = 13924 -> substrings 13, 39, 92, 24, 139, 392, 924, 1392, 3924 and 13924 are all non-palindromic.
%o (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};
%o 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};
%o for(n=0,200,if(noPalSub(n^2),print1(n", ")))
%Y Cf. A052062, A052063, A052064, A050741.
%K nonn,base
%O 1,3
%A _Patrick De Geest_, Jan 15 2000
%E Program and b-file from _Charles R Greathouse IV_, Sep 09 2009
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