A281301 Trajectory of 1000004999700144385 under the "Reverse and Add!" operation.

1000004999700144385, 6834415079694144386, 13668830049399288772, 41457129443403175403, 71914259877895350817, 143719619755790592734, 581014717313707510075, 1151030424627424920260, 1771324671891665221771, 3542550333873429453542, 5996099577656760005995

Offset

0,1

Comments

1000004999700144385 is the largest of the first 225 numbers that require exactly 259 steps to turn into a palindrome (see A281390). The sequence reaches a 119-digit palindrome after 259 steps (see b-file). The number was obtained empirically using computer algorithms and was not reported before.

Row 1000004999700144385 of the array in A243238. - Felix Fröhlich, Jan 21 2017

References

Popular Computing (Calabasas, CA), The 196 Problem, Vol. 3 (No. 30, Sep 1975).

Links

Sergei D. Shchebetov, Table of n, a(n) for n = 0..259

Jason Doucette, World Records

Yutaka Nishiyama, Numerical Palindromes and the 196 Problem, International Journal of Pure and Applied Mathematics, Volume 80, No. 3, 2012, 375-384.

R. Styer, The Palindromic Conjecture and the Fibonacci Sequence, Villanova University, 1986, 1-11.

C. W. Trigg, Palindromes by Addition, Mathematics Magazine, 40 (1967), 26-28.

C. W. Trigg, More on Palindromes by Reversal-Addition, Mathematics Magazine, 45 (1972), 184-186.

Wikipedia, Lychrel Number

196 and Other Lychrel Numbers, 196 and Lychrel Number

Index entries for sequences related to Reverse and Add!

Formula

a(n+1) = a(n) + rev(a(n)).

Example

a(1) = 1000004999700144385 + 5834410079994000001 = 6834415079694144386.

Mathematica

NestList[#+IntegerReverse[#]&, 1000004999700144385, 10] (* Harvey P. Dale, Dec 24 2021 *)

Prog

(PARI) terms(n) = my(x=1000004999700144385, i=0); while(1, print1(x, ", "); x=x+eval(concat(Vecrev(Str(x)))); i++; if(i==n, break))
/* Print initial 9 terms as follows: */
terms(9) \\ Felix Fröhlich, Jan 21 2017

Crossrefs

Cf. A023109, A033672, A065198, A065199, A065320, A065321, A065322, A065323, A065324, A065325, A065326, A065327, A070743, A072216, A072217, A072218, A243238, A281390.

Sequence in context: A256312 A173445 A281390 * A286481 A168334 A358020

Adjacent sequences: A281298 A281299 A281300 * A281302 A281303 A281304

Keyword

nonn,base

Author

Andrey S. Shchebetov and Sergei D. Shchebetov, Jan 21 2017

Extensions

a(9)-a(10) from Felix Fröhlich, Jan 21 2017

Status

approved