Search: id:A002113
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%I A002113 M0484 N0178
%S A002113 0,1,2,3,4,5,6,7,8,9,11,22,33,44,55,66,77,88,99,101,111,121,131,141,151,
%T A002113 161,171,181,191,202,212,222,232,242,252,262,272,282,292,303,313,323,333,
%U A002113 343,353,363,373,383,393,404,414,424,434,444,454,464,474,484,494,505,515
%N A002113 Palindromes in base 10.
%C A002113 n is a palindrome (i.e. a(k)=n for some k) iff n = A004086(n). - Reinhard 
               Zumkeller (reinhard.zumkeller(AT)gmail.com), Mar 10 2002
%C A002113 The g.f. -z*(1+10*z**9+10*z**10+81*z**11+9*z)/(8*z**10-9*z**9-9*z-1)/
               (z-1)**2 conjectured by S. Plouffe in his 1992 dissertation is wrong. 
               - N. J. A. Sloane (njas(AT)research.att.com), May 12 2008
%D A002113 Clifford A. Pickover, A Passion for Mathematics, Wiley, 2005; see p. 
               71.
%D A002113 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A002113 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%H A002113 N. J. A. Sloane, <a href="b002113.txt">List of first 1199 palindromes 
               (below 20000): Table of n, a(n) for n = 1..1199</a>
%H A002113 George Gregory, <a href="http://www.gallup.unm.edu/~smarandache/GSP.htm">
               Generalized Smarandache Palindromes</a>
%H A002113 S. Plouffe, <a href="http://www.lacim.uqam.ca/%7Eplouffe/articles/MasterThesis.pdf">
               Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures</
               a>, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 
               1992.
%H A002113 S. Plouffe, <a href="http://www.lacim.uqam.ca/%7Eplouffe/articles/FonctionsGeneratrices.pdf">
               1031 Generating Functions and Conjectures</a>, Universit\'{e} du 
               Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
%H A002113 E. A. Schmidt, <a href="http://eric-schmidt.com/eric/palindrome/index.html">
               Positive Integer Palindromes</a>
%H A002113 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               PalindromicNumber.html">Link to a section of The World of Mathematics.</
               a>
%p A002113 read transforms; t0:=[]; for n from 0 to 2000 do if digrev(n) = n then 
               t0:=[op(t0),n]; fi; od: t0;
%t A002113 palQ[n_Integer, base_Integer] := Module[{idn=IntegerDigits[n, base]}, 
               idn==Reverse[idn]]; then to generate any base-b sequence: Select[Range[1000], 
               palQ[ #, b]&]
%o A002113 (PARI) is_A002113(n) = vecextract(n=Vec(Vecsmall(Str(n))),"-1..1")==n 
               [From M. F. Hasler (MHasler(AT)univ-ag.fr), Nov 17 2008]
%Y A002113 Palindromes in bases 2 through 10: A006995, A014190, A014192, A029952, 
               A029953, A029954, A029803, A029955, A002113.
%Y A002113 Cf. A057148, A118594, A118595, A118596, A118597, A118598, A118599, A118600.
%Y A002113 Sequence in context: A043713 A110751 A147882 this_sequence A084982 A110785 
               A087992
%Y A002113 Adjacent sequences: A002110 A002111 A002112 this_sequence A002114 A002115 
               A002116
%K A002113 nonn,base,easy,nice,core
%O A002113 1,3
%A A002113 N. J. A. Sloane (njas(AT)research.att.com).

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