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A262188 Table read by rows: row n contains all distinct palindromes contained as substrings in decimal representation of n.

%I A262188 #14 Jul 11 2019 00:11:56
%S A262188 0,1,2,3,4,5,6,7,8,9,0,1,1,11,1,2,1,3,1,4,1,5,1,6,1,7,1,8,1,9,0,2,1,2,
%T A262188 2,22,2,3,2,4,2,5,2,6,2,7,2,8,2,9,0,3,1,3,2,3,3,33,3,4,3,5,3,6,3,7,3,
%U A262188 8,3,9,0,4,1,4,2,4,3,4,4,44,4,5,4,6,4
%N A262188 Table read by rows: row n contains all distinct palindromes contained as substrings in decimal representation of n.
%C A262188 Length of row n = A262190(n);
%C A262188 T(n,0) = A054054(n);
%C A262188 T(n,A262190(n)-1) = A047813(n).
%H A262188 Reinhard Zumkeller, <a href="/A262188/b262188.txt">Rows n = 0..10000 of triangle, flattened</a>
%H A262188 <a href="/index/Pac#palindromes">Index entries for sequences related to palindromes</a>
%e A262188 .     n |  T(n,*)           n |  T(n,*)              n |  T(n,*)
%e A262188 .  -----+-----------    ------+-------------    -------+--------------
%e A262188 .   100 |  0,1           1000 |  0,1             10000 |  0,1
%e A262188 .   101 |  0,1,101       1001 |  0,1,1001        10001 |  0,1,10001
%e A262188 .   102 |  0,1,2         1002 |  0,1,2           10002 |  0,1,2
%e A262188 .   103 |  0,1,3         1003 |  0,1,3           10003 |  0,1,3
%e A262188 .   104 |  0,1,4         1004 |  0,1,4           10004 |  0,1,4
%e A262188 .   105 |  0,1,5         1005 |  0,1,5           10005 |  0,1,5
%e A262188 .   106 |  0,1,6         1006 |  0,1,6           10006 |  0,1,6
%e A262188 .   107 |  0,1,7         1007 |  0,1,7           10007 |  0,1,7
%e A262188 .   108 |  0,1,8         1008 |  0,1,8           10008 |  0,1,8
%e A262188 .   109 |  0,1,9         1009 |  0,1,9           10009 |  0,1,9
%e A262188 .   110 |  0,1,11        1010 |  0,1,101         10010 |  0,1,1001
%e A262188 .   111 |  1,11,111      1011 |  0,1,11,101      10011 |  0,1,11,1001
%e A262188 .   112 |  1,2,11        1012 |  0,1,2,101       10012 |  0,1,2,1001
%e A262188 .   113 |  1,3,11        1013 |  0,1,3,101       10013 |  0,1,3,1001
%e A262188 .   114 |  1,4,11        1014 |  0,1,4,101       10014 |  0,1,4,1001
%e A262188 .   115 |  1,5,11        1015 |  0,1,5,101       10015 |  0,1,5,1001
%e A262188 .   116 |  1,6,11        1016 |  0,1,6,101       10016 |  0,1,6,1001
%e A262188 .   117 |  1,7,11        1017 |  0,1,7,101       10017 |  0,1,7,1001
%e A262188 .   118 |  1,8,11        1018 |  0,1,8,101       10018 |  0,1,8,1001
%e A262188 .   119 |  1,9,11        1019 |  0,1,9,101       10019 |  0,1,9,1001
%e A262188 .   120 |  0,1,2         1020 |  0,1,2           10020 |  0,1,2
%e A262188 .   121 |  1,2,121       1021 |  0,1,2           10021 |  0,1,2
%e A262188 .   122 |  1,2,22        1022 |  0,1,2,22        10022 |  0,1,2,22
%e A262188 .   123 |  1,2,3         1023 |  0,1,2,3         10023 |  0,1,2,3
%e A262188 .   124 |  1,2,4         1024 |  0,1,2,4         10024 |  0,1,2,4
%e A262188 .   125 |  1,2,5         1025 |  0,1,2,5         10025 |  0,1,2,5  .
%o A262188 (Haskell)
%o A262188 import Data.List (inits, tails, nub, sort)
%o A262188 a262188 n k = a262188_tabf !! n !! k
%o A262188 a262188_row n = a262188_tabf !! n
%o A262188 a262188_tabf = map (sort . nub . map (foldr (\d v -> 10 * v + d) 0) .
%o A262188    filter (\xs -> length xs == 1 || last xs > 0 && reverse xs == xs) .
%o A262188           concatMap (tail . inits) . tails) a031298_tabf
%o A262188 (PARI) A262188_row(n,b=10)=Set(concat(vector(logint(n+!n,b)+1,m,m=n\=b^(m>1);select(is_A002113,vector(logint(m+!m,b)+1,k,m%b^k))))) \\ _M. F. Hasler_, Jun 19 2018
%Y A262188 Cf. A262190 (row lengths), A054054 (left edge), A047813 (right edge), A136522, A002113.
%Y A262188 Cf. A031298, A218978.
%K A262188 nonn,tabf,base,look
%O A262188 0,3
%A A262188 _Reinhard Zumkeller_, Sep 14 2015