A008918 Numbers k such that 4*k = (k written backwards), k > 0.
2178, 21978, 219978, 2199978, 21782178, 21999978, 217802178, 219999978, 2178002178, 2197821978, 2199999978, 21780002178, 21978021978, 21999999978, 217800002178, 217821782178, 219780021978, 219978219978, 219999999978, 2178000002178, 2178219782178
Offset: 1
References
- Alfred S. Posamentier, Math Charmers, Tantalizing Tidbits for the Mind, Prometheus Books, NY, 2003, pages 41-42.
- D. Wells, The Penguin Dictionary of Curious and Interesting Numbers. Penguin Books, NY, 1986.
Links
- Ray Chandler, Table of n, a(n) for n = 1..10000 (first 200 terms from Vincenzo Librandi)
- C. A. Van Cott, The Integer Hokey Pokey, Math Horizons, Vol. 28, pp. 24-27, November 2020.
- L. H. Kendrick, Young Graphs: 1089 et al., J. Int. Seq. 18 (2015) 15.9.7.
- N. J. A. Sloane, 2178 And All That, arXiv:1307.0453 [math.NT], 2013; Fib. Quart., 52 (2014), 99-120.
- N. J. A. Sloane, 2178 And All That [Local copy]
Programs
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Mathematica
Rest@Select[FromDigits /@ Tuples[{0, 198}, 11], IntegerDigits[4*#] == Reverse@IntegerDigits[#] &] (* Arkadiusz Wesolowski, Aug 14 2012 *) 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 *) -
PARI
rev(n) = (eval(concat(Vecrev(Str(n))))); isok(n) = rev(n) == 4*n; \\ Michel Marcus, Sep 13 2015
Formula
Theorem (David W. Wilson): a(n) = 2*A001232(n).
Extensions
Corrected and extended by David W. Wilson Aug 15 1996, Dec 15 1997
a(20)-a(21) from Arkadiusz Wesolowski, Aug 14 2012
Comments