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 A029968 Palindromic in bases 13 and 10. 40
 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 222, 313, 353, 444, 575, 666, 797, 1111, 6776, 8778, 24542, 25452, 26362, 56265, 311113, 2377732, 2713172, 2832382, 2906092, 8864688, 10122101, 13055031, 20244202, 20944902, 23177132, 23877832 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 LINKS Robert G. Wilson v, Table of n, a(n) for n = 1..76 P. De Geest, Palindromic numbers beyond base 10 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, 13], AppendTo[l, a]], {n, 100000}]; l (* Robert G. Wilson v, Sep 03 2004 *) Select[Range[0, 10^5], PalindromeQ[#] && # == IntegerReverse[#, 13] &] (* Robert Price, Nov 09 2019 *) PROG (Python) from gmpy2 import digits def palQ(n, b): # check if n is a palindrome in base b s = digits(n, b) return s == s[::-1] def palQgen10(l): # generator of palindromes in base 10 of length <= 2*l if l > 0: yield 0 for x in range(1, l+1): for y in range(10**(x-1), 10**x): s = str(y) yield int(s+s[-2::-1]) for y in range(10**(x-1), 10**x): s = str(y) yield int(s+s[::-1]) A029968_list = [n for n in palQgen10(9) if palQ(n, 13)] # Chai Wah Wu, Dec 01 2014 CROSSREFS Cf. A007632, A007633, A029961, A029962, A029963, A029964, A029804, A029965, A029966, A029967, A029969, A029970, A029731, A097855, A099165. Sequence in context: A239090 A248889 A029967 * A097855 A250408 A029969 Adjacent sequences: A029965 A029966 A029967 * A029969 A029970 A029971 KEYWORD nonn,base AUTHOR Patrick De Geest STATUS approved

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Last modified May 30 12:02 EDT 2023. Contains 363050 sequences. (Running on oeis4.)