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A008918 Numbers k such that 4*k = (k written backwards), k > 0.

%I A008918 #55 May 24 2025 16:20:18
%S A008918 2178,21978,219978,2199978,21782178,21999978,217802178,219999978,
%T A008918 2178002178,2197821978,2199999978,21780002178,21978021978,21999999978,
%U A008918 217800002178,217821782178,219780021978,219978219978,219999999978,2178000002178,2178219782178
%N A008918 Numbers k such that 4*k = (k written backwards), k > 0.
%C A008918 There are Fibonacci(floor((k-2)/2)) terms with k digits (this is essentially A103609). - _Ray Chandler_, Oct 12 2017
%D A008918 Alfred S. Posamentier, Math Charmers, Tantalizing Tidbits for the Mind, Prometheus Books, NY, 2003, pages 41-42.
%D A008918 D. Wells, The Penguin Dictionary of Curious and Interesting Numbers. Penguin Books, NY, 1986.
%H A008918 Ray Chandler, <a href="/A008918/b008918.txt">Table of n, a(n) for n = 1..10000</a> (first 200 terms from Vincenzo Librandi)
%H A008918 C. A. Van Cott, <a href="https://doi.org/10.1080/10724117.2020.1809284">The Integer Hokey Pokey</a>, Math Horizons, Vol. 28, pp. 24-27, November 2020.
%H A008918 L. H. Kendrick, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL18/Kendrick/ken1.html">Young Graphs: 1089 et al.</a>, J. Int. Seq. 18 (2015) 15.9.7.
%H A008918 N. J. A. Sloane, <a href="http://arxiv.org/abs/1307.0453">2178 And All That</a>, arXiv:1307.0453 [math.NT], 2013; Fib. Quart., 52 (2014), 99-120.
%H A008918 N. J. A. Sloane, <a href="/A001232/a001232.pdf">2178 And All That</a> [Local copy]
%F A008918 Theorem (_David W. Wilson_): a(n) = 2*A001232(n).
%t A008918 Rest@Select[FromDigits /@ Tuples[{0, 198}, 11], IntegerDigits[4*#] == Reverse@IntegerDigits[#] &] (* _Arkadiusz Wesolowski_, Aug 14 2012 *)
%t A008918 okQ[t_]:=t==Reverse[t]&&First[t]!=0&&Min[Length/@Split[t]]>1; 198#&/@ Flatten[ Table[FromDigits/@Select[Tuples[{0,1},n],okQ],{n,20}]] (* _Harvey P. Dale_, Jul 03 2013 *)
%o A008918 (PARI) rev(n) = (eval(concat(Vecrev(Str(n)))));
%o A008918 isok(n) = rev(n) == 4*n; \\ _Michel Marcus_, Sep 13 2015
%Y A008918 Cf. A001232, A193434, A008918, A008919, A222814, A222815, A031877.
%K A008918 nonn,base
%O A008918 1,1
%A A008918 _N. J. A. Sloane_
%E A008918 Corrected and extended by _David W. Wilson_ Aug 15 1996, Dec 15 1997
%E A008918 a(20)-a(21) from _Arkadiusz Wesolowski_, Aug 14 2012