login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A029731 Palindromic in bases 10 and 16. 37
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

Patrick 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

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

Patrick De Geest

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified May 24 19:14 EDT 2020. Contains 334580 sequences. (Running on oeis4.)