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Search: id:A007632
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| A007632 |
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Numbers that are palindromic in bases 2 and 10.
(Formerly M2406)
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+0
23
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| 0, 1, 3, 5, 7, 9, 33, 99, 313, 585, 717, 7447, 9009, 15351, 32223, 39993, 53235, 53835, 73737, 585585, 1758571, 1934391, 1979791, 3129213, 5071705, 5259525, 5841485, 13500531, 719848917, 910373019, 939474939, 1290880921, 7451111547
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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Charlton Harrison found a new record binary-decimal palindrome 11000101111000010101010110100001110100000100000101110000101101010101000011110100011_2 = 7475703079870789703075747_10 on Dec 01 2001. The binary string contains 83 digits! Since then he has added twenty more terms. - Robert G. Wilson v Jul 03 2006
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
M. R. Calandra, Integers which are palindromic in both decimal and binary notation, J. Rec. Math., 18 (No. 1, 1985-1986), 47.
S. Pilpel, Some More Double Palindromic Integers, J. Rec. Math., 18 (1985), 174-176.
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LINKS
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Robert G. Wilson v, Table of n, a(n) for n = 1..118
P. De Geest, Palindromic numbers beyond base 10
Charlton Harrison, Binary/Decimal Palindromes
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MATHEMATICA
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NextPalindrome[n_] := Block[{l = Floor[ Log[10, n] + 1], idn = IntegerDigits[n]}, If[ Union[ idn] == {9}, Return[n + 2], If[l < 2, Return[n + 1], If[ FromDigits[ Reverse[ Take[idn, Ceiling[l/2]] ]] > FromDigits[ Take[idn, -Ceiling[l/2]]], FromDigits[ Join[ Take[idn, Ceiling[l/2]], Reverse[ Take[idn, Floor[l/2]]] ]], idfhn = FromDigits[ Take[idn, Ceiling[l/2]]] + 1; idp = FromDigits[ Join[ IntegerDigits[ idfhn], Drop[ Reverse[ IntegerDigits[ idfhn]], Mod[l, 2]] ]] ]] ]]; palQ[n_Integer, base_Integer]:= Block[{idn = IntegerDigits[n, base]}, idn == Reverse[idn]]; l = {0}; a = 0; Do[a = NextPalindrome[a]; If[ palQ[a, 2], AppendTo[l, a]], {n, 1000000}]; l (from Robert G. Wilson v Sep 30 2004)
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CROSSREFS
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For number of terms less than or equal to 10^n, see A120764.
Cf. A007633, A029961, A029962, A029963, A029964, A029804, A029965, A029966, A029967, A029968, A029969, A029970, A029731, A097855, A099165.
Sequence in context: A119252 A141708 A081434 this_sequence A117996 A092046 A085951
Adjacent sequences: A007629 A007630 A007631 this_sequence A007633 A007634 A007635
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KEYWORD
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base,nonn,nice
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Mira Bernstein, Robert G. Wilson v (rgwv(AT)rgwv.com)
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EXTENSIONS
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One more term from George Russell (ger(AT)tzi.de), Nov 20 2000. Two further terms from Harvey P. Dale (hpd1(AT)nyu.edu), Mar 09 2001.
Further terms from George Russell (ger(AT)tzi.de), Nov 02 2001
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