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A029967 Palindromic in bases 12 and 10. 39
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 181, 555, 616, 676, 737, 797, 1111, 8008, 35953, 43934, 88888, 646646, 3192913, 5641465, 8364638, 9963699, 133373331, 139979931, 293373392, 520020025, 713171317, 796212697, 1393223931 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Robert G. Wilson v, Table of n, a(n) for n = 1..57

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, 12], AppendTo[l, a]], {n, 400000}]; l (* Robert G. Wilson v, Sep 30 2004 *)

Select[Range[0, 10^5],

PalindromeQ[#] && # == IntegerReverse[#, 12] &] (* 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])

A029967_list = [n for n in palQgen10(5) if palQ(n, 12)] # Chai Wah Wu, Dec 01 2014

CROSSREFS

Cf. A007632, A007633, A029961, A029962, A029963, A029964, A029804, A029965, A029966, A029968, A029969, A029970, A029731, A097855, A099165.

Sequence in context: A249516 A239090 A248889 * A029968 A097855 A250408

Adjacent sequences:  A029964 A029965 A029966 * A029968 A029969 A029970

KEYWORD

nonn,base

AUTHOR

Patrick De Geest

STATUS

approved

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Last modified December 8 17:36 EST 2019. Contains 329865 sequences. (Running on oeis4.)