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A286481 Numbers which require exactly 260 'Reverse and Add' steps to reach a palindrome 2
1003062289999939142, 1003062299899939142, 1003062389989939142, 1003062399889939142, 1003062489979939142, 1003062499879939142, 1003062589969939142, 1003062599869939142, 1003062689959939142, 1003062699859939142, 1003062789949939142, 1003062799849939142, 1003062889939939142, 1003062899839939142, 1003062989929939142, 1003062999829939142 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The sequence starts with 1003062289999939142 (the 19-digit number discovered by Vaughn Suite on Mar 19 2006) and continues for another 430079 terms (none previously reported) each turning into a 119-digit palindrome after 260 steps until the sequence ends with 3419399999822603000 (see a-file). No further numbers beyond 3419399999822603000 belonging to the same sequence exist. The sequence was predicted theoretically and found empirically using computer modeling algorithms. For the first 100 terms of the sequence see b-file.

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 = 1..99

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.

Sergei D. Shchebetov, 430080 terms (zipped file)

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) = 1003062289999939142 + 2419399999822603001 = 3422462289822542143

CROSSREFS

Cf. A023109, A033672, A065198, A065199, A065320, A065321, A065322, A065323, A065324, A065325, A065326, A065327, A070743, A072216, A072217, A072218, A281301, A281390, A281506, A281507, A281508, A281509.

Sequence in context: A173445 A281390 A281301 * A168334 A095434 A276377

Adjacent sequences:  A286478 A286479 A286480 * A286482 A286483 A286484

KEYWORD

nonn,base

AUTHOR

Andrey S. Shchebetov and Sergei D. Shchebetov, May 12 2017

STATUS

approved

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Last modified August 18 01:45 EDT 2019. Contains 326059 sequences. (Running on oeis4.)