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 A029731 Palindromic in bases 10 and 16. 36
 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 353, 626, 787, 979, 1991, 3003, 39593, 41514, 90209, 94049, 96369, 98689, 333333, 512215, 666666, 749947, 845548, 1612161, 2485842, 5614165, 6487846, 9616169, 67433476, 90999909, 94355349, 94544549, 119919911 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 LINKS Robert G. Wilson v, Table of n, a(n) for n = 1..81 P. De Geest, Palindromic numbers beyond base 10 MAPLE N:= 9: # to get all terms with up to N decimal digits qpali:= proc(k, b) local L; L:= convert(k, base, b); if L = ListTools:-Reverse(L) then k else NULL fi end proc: digrev:= proc(k, b) local L, n; L:= convert(k, base, b); n:= nops(L); add(L[i]*b^(n-i), i=1..n); end proc: Res:= \$0..9: for d from 2 to N do   if d::even then     m:= d/2;     Res:= Res, seq(qpali(n*10^m + digrev(n, 10), 16), n=10^(m-1)..10^m-1);   else     m:= (d-1)/2;     Res:= Res, seq(seq(qpali(n*10^(m+1)+y*10^m+digrev(n, 10), 16), y=0..9), n=10^(m-1)..10^m-1);   fi od: Res; # Robert Israel, Nov 23 2014 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, 16], AppendTo[l, a]], {n, 20000}]; l (* Robert G. Wilson v, Sep 03 2004 *) A029731Q = PalindromeQ@# && IntegerReverse[#, 16] == # &; Select[Range[10^5], A029731Q] (* JungHwan Min, Mar 02 2017 *) Select[Range[10^7], Times @@ Boole@ Map[# == Reverse@ # &, {IntegerDigits@ #, IntegerDigits[#, 16]}] > 0 &] (* Michael De Vlieger, Mar 03 2017 *) PROG (Python) def palQ16(n): # check if n is a palindrome in base 16 ....s = hex(n)[2:] ....return s == s[::-1] def palQgen10(l): # unordered generator of palindromes of length <= 2*l ....if l > 0: ........yield 0 ........for x in range(1, 10**l): ............s = str(x) ............yield int(s+s[-2::-1]) ............yield int(s+s[::-1]) A029731_list = sorted([n for n in palQgen10(6) if palQ16(n)]) # Chai Wah Wu, Nov 25 2014 CROSSREFS Cf. A007632, A007633, A029961, A029962, A029963, A029964, A029804, A029965, A029966, A029967, A029968, A029969, A029970, A097855, A099165. Sequence in context: A097855 A250408 A029969 * A248899 A029970 A143265 Adjacent sequences:  A029728 A029729 A029730 * A029732 A029733 A029734 KEYWORD nonn,base AUTHOR STATUS approved

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