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 A007633 Palindromic in bases 3 and 10. (Formerly M1164) 40
 0, 1, 2, 4, 8, 121, 151, 212, 242, 484, 656, 757, 29092, 48884, 74647, 75457, 76267, 92929, 93739, 848848, 1521251, 2985892, 4022204, 4219124, 4251524, 4287824, 5737375, 7875787, 7949497, 27711772, 83155138, 112969211, 123464321 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 REFERENCES J. Meeus, Multibasic palindromes, J. Rec. Math., 18 (No. 3, 1985-1986), 168-173. N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS Robert Israel and Robert G. Wilson v, Table of n, a(n) for n = 1..65 (first 41 terms from Robert Israel) M. R. Calandra, Integers which are palindromic in both decimal and binary notation, J. Rec. Math., 18 (No. 1, 1985-1986), 47. (Annotated scanned copy) [With scan of J. Rec. Math. 18.3 (1985), pp. 168-173] MAPLE ND:= 12;  # to get all terms with <= ND decimal digits rev10:= proc(n) option remember;   rev10(floor(n/10)) + (n mod 10)*10^ilog10(n) end; for i from 0 to 9 do rev10(i):= i od: rev3:= proc(n) option remember;   rev3(floor(n/3)) + (n mod 3)*3^ilog[3](n) end; for i from 0 to 2 do rev3(i):= i od: pali3:= n -> rev3(n) = n; count:= 1: A[1]:= 0: for d from 1 to ND do   d1:= ceil(d/2);   for x from 10^(d1-1) to 10^d1 - 1 do     if d::even then y:= x*10^d1+rev10(x)     else y:= x*10^(d1-1)+rev10(floor(x/10));     fi;     if pali3(y) then        count:= count+1;        A[count]:= y;     fi   od: od: seq(A[i], i=1..count); # Robert Israel, Apr 20 2014 MATHEMATICA Do[ a = IntegerDigits[n]; b = IntegerDigits[n, 3]; If[a == Reverse[a] && b == Reverse[b], Print[n] ], {n, 0, 10^9} ] 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, 4], AppendTo[l, a]], {n, 100000}]; l (* Robert G. Wilson v, Sep 30 2004 *) PROG (Python) from itertools import chain from gmpy2 import digits A007633_list = sorted([n for n in chain((int(str(x)+str(x)[::-1]) for x in range(1, 10**6)), (int(str(x)+str(x)[-2::-1]) for x in range(10**6))) if digits(n, 3) == digits(n, 3)[::-1]]) # Chai Wah Wu, Nov 23 2014 CROSSREFS Cf. A007632, A029961, A029962, A029963, A029964, A029804, A029965, A029966, A029967, A029968, A029969, A029970, A029731, A097855, A099165. Sequence in context: A018694 A129661 A018713 * A018777 A130693 A286523 Adjacent sequences:  A007630 A007631 A007632 * A007634 A007635 A007636 KEYWORD nonn,base AUTHOR STATUS approved

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Last modified March 24 23:28 EDT 2018. Contains 301219 sequences. (Running on oeis4.)