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 A248889 Palindromic in base 10 and 18. 2
 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 171, 323, 343, 505, 595, 686, 848, 1661, 2112, 3773, 23332, 46664, 69996, 262262, 583385, 782287, 859958, 981189, 1254521, 1403041, 1832381, 39388393, 54411445, 55499455, 88844888, 118919811, 191010191 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS a(54) > 10^12. LINKS M. Fiorentini and Chai Wah Wu, Table of n, a(n) for n = 1..68 a(n) for n = 1..53 from M. Fiorentini. EXAMPLE 848 in decimal is 2B2 in base 18, so 848 is in the sequence. 1661 in decimal is 525 in base 18, so 1661 is in the sequence. 1771 in decimal is 587 in base 18, which is not a palindrome, so 1771 is not in the sequence. MAPLE IsPalindromic := proc(n, Base)     local Conv, i;     Conv := convert(n, base, Base);     for i from 1 to nops(Conv) / 2 do         if Conv [i] <> Conv [nops(Conv) + 1 - i] then             return false;         fi:     od:     true; end proc: Base := 18; A := []; for i from 1 to 10^6 do:    S := convert(i, base, 10);    V := 0;    if i mod 10 = 0 then       next;    fi;    for j from 1 to nops(S) do:       V := V * 10 + S [j];    od:    for j from 0 to 10 do:       V1 := V * 10^(nops(S) + j) + i;       if IsPalindromic(V1, Base) then          A := [op(A), V1];       fi;    od:    V1 := (V - (V mod 10)) * 10^(nops(S) - 1) + i;    if IsPalindromic(V1, Base) then       A := [op(A), V1];    fi; od: sort(A); MATHEMATICA palindromicQ[n_, b_:10] := TrueQ[IntegerDigits[n, b] == Reverse[IntegerDigits[n, b]]]; Select[Range[0, 499], palindromicQ[#] && palindromicQ[#, 18] &] (* Alonso del Arte, Mar 21 2015 *) PROG (PARI) isok(n) = (n==0) || ((d = digits(n, 10)) && (Vecrev(d) == d) && (d = digits(n, 18)) && (Vecrev(d) == d)); \\ Michel Marcus, Mar 14 2015 (MAGMA) [n: n in [0..2*10^7] | Intseq(n) eq Reverse(Intseq(n)) and Intseq(n, 18) eq Reverse(Intseq(n, 18))]; // Vincenzo Librandi, Mar 21 2015 (Python) def palgen10(l): # generator of palindromes of length <= 2*l ....if l > 0: ........yield 0 ........for x in range(1, l+1): ............n = 10**(x-1) ............n2 = n*10 ............for y in range(n, n2): ................s = str(y) ................yield int(s+s[-2::-1]) ............for y in range(n, n2): ................s = str(y) ................yield int(s+s[::-1]) def palcheck(n, b): # check if n is a palindrome in base b ....s = digits(n, b) ....return s == s[::-1] A248889_list = [n for n in palgen10(9) if palcheck(n, 18)] # Chai Wah Wu, Mar 23 2015 CROSSREFS Cf. A007632, A007633, A029961, A029962, A029963, A029964, A029965, A029966, A029967, A029968, A029969, A029970, A028731, A097855, A248899 Sequence in context: A117057 A249516 A239090 * A029967 A029968 A097855 Adjacent sequences:  A248886 A248887 A248888 * A248890 A248891 A248892 KEYWORD nonn,base AUTHOR Mauro Fiorentini, Mar 05 2015 STATUS approved

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Last modified May 31 15:19 EDT 2020. Contains 334748 sequences. (Running on oeis4.)