

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
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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 ndigit 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) = digitwise 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^(i1)+(2*i1<l)*10^(li))~; forvec(v=vector((l+1)\2, i, [l>1&&i==1, 2]), print1((v+v\2*6)*u", ")))} \\ The nth 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

N. J. A. Sloane.


EXTENSIONS

More terms from Robert G. Wilson v, Nov 16 2005


STATUS

approved



