A248889 Palindromic in base 10 and 18.
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
Offset: 1
Examples
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.
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.
Crossrefs
Programs
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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
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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 *)
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PARI
isok(n) = (n==0) || ((d = digits(n, 10)) && (Vecrev(d) == d) && (d = digits(n, 18)) && (Vecrev(d) == d)); \\ Michel Marcus, Mar 14 2015
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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
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