Search: id:A007632
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%I A007632 M2406
%S A007632 0,1,3,5,7,9,33,99,313,585,717,7447,9009,15351,32223,39993,53235,53835,
%T A007632 73737,585585,1758571,1934391,1979791,3129213,5071705,5259525,5841485,
%U A007632 13500531,719848917,910373019,939474939,1290880921,7451111547
%N A007632 Numbers that are palindromic in bases 2 and 10.
%C A007632 Charlton Harrison found a new record binary-decimal palindrome 1100010111100001010101011010000111010000010000\
               0101110000101101010101000011110100011_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
%D A007632 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A007632 M. R. Calandra, Integers which are palindromic in both decimal and binary 
               notation, J. Rec. Math., 18 (No. 1, 1985-1986), 47.
%D A007632 S. Pilpel, Some More Double Palindromic Integers, J. Rec. Math., 18 (1985), 
               174-176.
%H A007632 Robert G. Wilson v, <a href="b007632.txt">Table of n, a(n) for n = 1..118</
               a>
%H A007632 P. De Geest, <a href="http://www.worldofnumbers.com/nobase10.htm">Palindromic 
               numbers beyond base 10</a>
%H A007632 Charlton Harrison, <a href="http://bach.dynet.com/palin/">Binary/Decimal 
               Palindromes</a>
%t A007632 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)
%Y A007632 For number of terms less than or equal to 10^n, see A120764.
%Y A007632 Cf. A007633, A029961, A029962, A029963, A029964, A029804, A029965, A029966, 
               A029967, A029968, A029969, A029970, A029731, A097855, A099165.
%Y A007632 Sequence in context: A119252 A141708 A081434 this_sequence A117996 A092046 
               A085951
%Y A007632 Adjacent sequences: A007629 A007630 A007631 this_sequence A007633 A007634 
               A007635
%K A007632 base,nonn,nice
%O A007632 1,3
%A A007632 N. J. A. Sloane (njas(AT)research.att.com), Mira Bernstein, Robert G. 
               Wilson v (rgwv(AT)rgwv.com)
%E A007632 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.
%E A007632 Further terms from George Russell (ger(AT)tzi.de), Nov 02 2001

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