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A173551 Palindromes in base 10 and in one other base (from 2 to 9). 2
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 33, 55, 88, 99, 111, 121, 141, 151, 171, 191, 212, 242, 252, 282, 292, 313, 333, 343, 373, 393, 414, 434, 464, 484, 555, 585, 626, 646, 656, 666, 676, 717, 757, 777, 787, 868, 939, 1221, 1441, 3663, 6886, 7447, 7667, 7777, 7997, 8778, 9009 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Robert G. Wilson v, Table of n, a(n) for n = 1..510

Edray Herber Goins, Palindromes in Different Bases: A Conjecture of J. Ernest Wilkins, Integers 9 (2009), 725-734.

EXAMPLE

a(11) = 33 = {1,0,0,0,1} in base 2;

a(99) = 909909 = {3, 1, 3, 0, 0, 3, 1, 3} in base 6;

a(98) = 848848 = {1, 1, 2, 1, 0, 1, 0, 1, 0, 1, 2, 1, 1} in base 3.

MAPLE

N:= 6: # to get all terms of up to N digits

digrev:= proc(n) local L;

  L:= convert(n, base, 10);

  add(L[-i]*10^(i-1), i=1..nops(L));

end proc:

basepali:= proc(b, n)

      local L;

      L:= convert(n, base, b);

      evalb(L = ListTools:-Reverse(L))

end proc:

Res:= $0..9:

for d from 2 to N do

  if d::even then

    m:= d/2;

    Res:= Res, seq(n*10^m + digrev(n), n=10^(m-1)..10^m-1);

  else

    m:= (d-1)/2;

    Res:= Res, seq(seq(n*10^(m+1)+y*10^m+digrev(n), y=0..9), n=10^(m-1)..10^m-1);

  fi

od:

select(t -> ormap(basepali, [$2..9], t), [Res]); # Robert Israel, Oct 15 2014

MATHEMATICA

palQ[n_Integer, base_Integer]:=Block[{}, Reverse[idn=IntegerDigits[n, base]]==idn]

; Select[Range[0, 10000], palQ[#, 10] && (palQ[#, 2] || palQ[#, 3] || palQ[#, 4] || palQ[#, 5] || palQ[#, 6] || palQ[#, 7] || palQ[#, 8] || palQ[#, 9]) &] (* Robert G. Wilson v, Oct 10 2014 *)

CROSSREFS

Cf. A165932.

Sequence in context: A004849 A261279 A295638 * A271534 A072482 A254958

Adjacent sequences:  A173548 A173549 A173550 * A173552 A173553 A173554

KEYWORD

nonn,base

AUTHOR

José María Grau Ribas, Feb 21 2010

EXTENSIONS

Term 0 prepended by Robert G. Wilson v, Oct 10 2014

STATUS

approved

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Last modified August 18 13:12 EDT 2019. Contains 326100 sequences. (Running on oeis4.)