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

1,1

Comments

There are Fibonacci(floor((k-2)/2)) terms with k digits (this is essentially A103609). - Ray Chandler, Oct 12 2017

References

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.

Formula

Theorem (David W. Wilson): A008918(n) = 2*A001232(n).

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 *)

Prog

(PARI) rev(n) = (eval(concat(Vecrev(Str(n)))));
isok(n) = rev(n) == 4*n; \\ Michel Marcus, Sep 13 2015

Crossrefs

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

Sequence in context: A157476 A157853 A072141 * A262792 A035770 A107566

Adjacent sequences: A008915 A008916 A008917 * A008919 A008920 A008921

Keyword

nonn,base

Author

N. J. A. Sloane

Extensions

Corrected and extended by David W. Wilson Aug 15 1996, Dec 15 1997

a(20)-a(21) from Arkadiusz Wesolowski, Aug 14 2012

Status

approved