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A008918 Numbers k such that 4*k = (k written backwards), k > 0. 13

%I #48 Jul 01 2021 23:42:58

%S 2178,21978,219978,2199978,21782178,21999978,217802178,219999978,

%T 2178002178,2197821978,2199999978,21780002178,21978021978,21999999978,

%U 217800002178,217821782178,219780021978,219978219978,219999999978,2178000002178,2178219782178

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

%C There are Fibonacci(floor((k-2)/2)) terms with k digits (this is essentially A103609). - _Ray Chandler_, Oct 12 2017

%D D. Wells, The Penguin Dictionary of Curious and Interesting Numbers. Penguin Books, NY, 1986.

%H Ray Chandler, <a href="/A008918/b008918.txt">Table of n, a(n) for n = 1..10000</a> (first 200 terms from Vincenzo Librandi)

%H 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 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 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.

%F Theorem (_David W. Wilson_): A008918(n) = 2*A001232(n).

%t Rest@Select[FromDigits /@ Tuples[{0, 198}, 11], IntegerDigits[4*#] == Reverse@IntegerDigits[#] &] (* _Arkadiusz Wesolowski_, Aug 14 2012 *)

%t 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 (PARI) rev(n) = (eval(concat(Vecrev(Str(n)))));

%o isok(n) = rev(n) == 4*n; \\ _Michel Marcus_, Sep 13 2015

%Y Cf. A001232, A193434, A008918, A008919, A222814, A222815, A031877.

%K nonn,base

%O 1,1

%A _N. J. A. Sloane_

%E Corrected and extended by _David W. Wilson_ Aug 15 1996, Dec 15 1997

%E a(20)-a(21) from _Arkadiusz Wesolowski_, Aug 14 2012

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Last modified March 28 09:04 EDT 2024. Contains 371240 sequences. (Running on oeis4.)