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Search: id:A002113
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| A002113 |
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Palindromes in base 10.
(Formerly M0484 N0178)
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+0
198
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| 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, 161, 171, 181, 191, 202, 212, 222, 232, 242, 252, 262, 272, 282, 292, 303, 313, 323, 333, 343, 353, 363, 373, 383, 393, 404, 414, 424, 434, 444, 454, 464, 474, 484, 494, 505, 515
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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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
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
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REFERENCES
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Clifford A. Pickover, A Passion for Mathematics, Wiley, 2005; see p. 71.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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N. J. A. Sloane, List of first 1199 palindromes (below 20000): Table of n, a(n) for n = 1..1199
George Gregory, Generalized Smarandache Palindromes
S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
S. Plouffe, 1031 Generating Functions and Conjectures, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
E. A. Schmidt, Positive Integer Palindromes
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
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MAPLE
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read transforms; t0:=[]; for n from 0 to 2000 do if digrev(n) = n then t0:=[op(t0), n]; fi; od: t0;
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MATHEMATICA
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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]&]
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PROGRAM
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(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]
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CROSSREFS
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Palindromes in bases 2 through 10: A006995, A014190, A014192, A029952, A029953, A029954, A029803, A029955, A002113.
Cf. A057148, A118594, A118595, A118596, A118597, A118598, A118599, A118600.
Adjacent sequences: A002110 A002111 A002112 this_sequence A002114 A002115 A002116
Sequence in context: A043713 A110751 A147882 this_sequence A084982 A110785 A087992
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KEYWORD
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nonn,base,easy,nice,core
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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