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A029731 Palindromic in bases 10 and 16. 15
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 *)

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 * A029970 A143265 A109841

Adjacent sequences:  A029728 A029729 A029730 * A029732 A029733 A029734

KEYWORD

nonn,base

AUTHOR

Patrick De Geest

STATUS

approved

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Last modified December 22 18:48 EST 2014. Contains 252365 sequences.