The OEIS is supported by the many generous donors to the OEIS Foundation.

 Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 60th year, we have over 367,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”). Other ways to Give
 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A085305 Numbers such that first reversing digits and then squaring equals the result of first squaring and then reversing. 8
 0, 1, 2, 3, 11, 12, 13, 21, 22, 31, 101, 102, 103, 111, 112, 113, 121, 122, 201, 202, 211, 212, 221, 301, 311, 1001, 1002, 1003, 1011, 1012, 1013, 1021, 1022, 1031, 1101, 1102, 1103, 1111, 1112, 1113, 1121, 1122, 1201, 1202, 1211, 1212, 1301, 2001, 2002, 2011 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Only digits {0, 1, 2, 3} seem to arise. Numbers (other than 0) that end in zero are excluded. - N. J. A. Sloane, Mar 20 2010 REFERENCES David Wells, The Dictionary of Curious and Interesting Numbers. London: Penguin Books (1997): p. 124. LINKS Reinhard Zumkeller, Table of n, a(n) for n = 1..1000 Index entry for sequences related to reversing digits of squares FORMULA Solutions to rev(x^2) = rev(x)^2. EXAMPLE n = 13 is a term because 31^2 = 961 = rev(169) = rev(13^2) = rev(rev(31)^2). MATHEMATICA rt[x_] := tn[Reverse[IntegerDigits[x]]] Do[s = rt[n^2]; s1=rt[n]^2; If[Equal[s, s1]&&!Equal[Mod[n, 10], 0], Print[{n, s, rt[s1]}]], {n, 0, 1000000}] (* Second program: *) Select[Range[0, 1999], Mod[#, 10] != 0 && FromDigits[Reverse[IntegerDigits[#^2]]] == FromDigits[Reverse[IntegerDigits[#]]]^2 &] (* Alonso del Arte, Oct 08 2012; corrected by Jean-François Alcover, Jan 11 2021 *) PROG a085305 n = a085305_list !! (n-1) a085305_list = 0 : filter (\x -> x `mod` 10 > 0 && a004086 (x^2) == (a004086 x)^2) [1..] -- Reinhard Zumkeller, Jul 08 2011 (Magma) [0] cat [ m: n in [1..1810] | Reverse(Intseq(m^2)) eq Intseq(Seqint(Reverse(Intseq(m)))^2) where m is n+Floor((n-1)/9) ]; // Bruno Berselli, Jul 08 2011 (PARI) isok(x) = (x==0) || ((x%10) && fromdigits(Vecrev(digits(x^2))) == fromdigits(Vecrev(digits(x)))^2); \\ Michel Marcus, Jan 11 2021 CROSSREFS Cf. A085306. See A061909 for another version. Sequence in context: A007932 A334054 A035122 * A189818 A116032 A116029 Adjacent sequences: A085302 A085303 A085304 * A085306 A085307 A085308 KEYWORD base,nonn AUTHOR Labos Elemer, Jun 27 2003 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 10 04:38 EST 2023. Contains 367699 sequences. (Running on oeis4.)