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A007632
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Numbers that are palindromic in bases 2 and 10.
(Formerly M2406)
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24
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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; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| 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
Intersection of A002113 and A006995. [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Jan 22 2012, Feb 07 2010]
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REFERENCES
| 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.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| Robert G. Wilson v, Charlton Harrison, Table of n, a(n) for n = 1..122
P. De Geest, Palindromic numbers beyond base 10
Charlton Harrison, Binary/Decimal Palindromes
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MATHEMATICA
| 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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PROG
| (Haskell)
a007632 n = a007632_list !! (n-1)
a007632_list = filter ((== 1) . a178225) a002113_list
-- Reinhard Zumkeller, Jan 22 2012
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CROSSREFS
| 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 * A117996 A092046 A085951
Adjacent sequences: A007629 A007630 A007631 * A007633 A007634 A007635
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KEYWORD
| base,nonn,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Mira Bernstein, Robert G. Wilson v (rgwv(AT)rgwv.com)
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EXTENSIONS
| 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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