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 A006072 Numbers with mirror symmetry about middle. (Formerly M4481) 11
 0, 1, 8, 11, 88, 101, 111, 181, 808, 818, 888, 1001, 1111, 1881, 8008, 8118, 8888, 10001, 10101, 10801, 11011, 11111, 11811, 18081, 18181, 18881, 80008, 80108, 80808, 81018, 81118, 81818, 88088, 88188, 88888, 100001, 101101, 108801, 110011 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Apparently this sequence and A111065 have the same parity. - Jeremy Gardiner, Oct 15 2005 Obviously, terms of this sequence also have the same parity (and also digital sum mod 6) as those of A118594, see below. - M. F. Hasler, May 08 2013 The number of n-digit terms is given by A225367 -- which counts palindromes in base 3, A118594. The terms here are the base 3 palindromes considered there, with 2 replaced by 8 (which means this sequence A006072 arises from A118594 not only by taking the 3rd power of each digit, but also by superposing the number with its horizontal or vertical reflection, somehow remarkably given the symmetry of numbers considered here). - M. F. Hasler, May 05 2013 [Part of the comment moved from A225367 to here on May 08 2013] REFERENCES N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS Vincenzo Librandi, Table of n, a(n) for n = 1..1450 Eric Weisstein's World of Mathematics, Tetradic Number FORMULA a(n) = digit-wise application of A000578 to A118594(n). - M. F. Hasler, May 08 2013 MATHEMATICA 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]]]]]]]]; np = 0; t = {0}; Do[np = NextPalindrome[np]; If[Union[Join[{0, 1, 8}, IntegerDigits[np]]] == {0, 1, 8}, AppendTo[t, np]], {n, 1150}]; t (* Robert G. Wilson v *) TetrNumsUpTo10powerK[k_]:= Select[FromDigits/@ Tuples[{0, 1, 8}, k], IntegerDigits[#] == Reverse[IntegerDigits[#]] &]; TetrNumsUpTo10powerK[7] (* Mikk Heidemaa, May 21 2017 *) PROG (PARI) {for(l=1, 5, u=vector((l+1)\2, i, 10^(i-1)+(2*i-11&&i==1, 2]), print1((v+v\2*6)*u", ")))} \\ The n-th term could be produced by using (partial sums of) A225367 to skip all shorter terms, and then skipping the adequate number of vectors v until n is reached.  - M. F. Hasler, May 05 2013 CROSSREFS Subsequence of A000787. Sequence in context: A188000 A167621 A289287 * A196173 A074042 A140478 Adjacent sequences:  A006069 A006070 A006071 * A006073 A006074 A006075 KEYWORD base,nonn,easy AUTHOR EXTENSIONS More terms from Robert G. Wilson v, Nov 16 2005 STATUS approved

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Last modified September 29 21:59 EDT 2020. Contains 337432 sequences. (Running on oeis4.)