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 A173551 Palindromes in base 10 and in at least 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 *) palQ[n_, b_]:=Module[{idb=IntegerDigits[n, b]}, idb==Reverse[idb]]; pal2to9[n_]:=Total[Boole[ Table[palQ[n, b], {b, 2, 9}]]]>0; Select[Range[0, 10000], PalindromeQ[#]&&pal2to9[#]&] (* Harvey P. Dale, Jul 13 2023 *) CROSSREFS Cf. A165932. Sequence in context: A261279 A295638 A357195 * 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 Definition clarified by Harvey P. Dale, Jul 13 2023 STATUS approved

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Last modified April 16 18:00 EDT 2024. Contains 371750 sequences. (Running on oeis4.)