A281506 -id:A281506 - cp's OEIS frontend

A281507 Trajectory of 1186061987030929990 under the "Reverse and Add!" operation.

1186061987030929990, 2185352294922536801, 3271704589845072613, 6434410079699144336, 12768830049399288682, 41457129443403175403, 71914259877895350817, 143719619755790592734, 581014717313707510075, 1151030424627424920260, 1771324671891665221771

Offset: 0

Andrey S. Shchebetov and Sergei D. Shchebetov, Jan 23 2017

1186061987030929990 is the largest of the first 126 numbers that require exactly 261 steps to turn into a palindrome (see A281506). The sequence reaches a 119-digit palindrome after 261 steps (see b-file). The number was obtained empirically using computer algorithms and was not reported before.

			a(1) = 1186061987030929990 + 999290307891606811 = 2185352294922536801.

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

Sergei D. Shchebetov, Table of n, a(n) for n = 0..261
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!

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

k:=1186061987030929990; [n eq 1 select k else Self(n-1) + Seqint(Reverse(Intseq(Self(n-1)))): n in [1..20]]; // Bruno Berselli, Jan 23 2017

NestList[#+IntegerReverse[#]&,1186061987030929990,20] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jan 17 2019 *)

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

A281508 Numbers requiring exactly 261 'Reverse and Add' steps to reach a palindrome.

Original entry on oeis.org

1999290307891606810, 1999290317791606810, 1999290327691606810, 1999290337591606810, 1999290347491606810, 1999290357391606810, 1999290367291606810, 1999290377191606810, 1999290387091606810, 1999290407881606810, 1999290417781606810, 1999290427681606810, 1999290437581606810

Offset: 1

Andrey S. Shchebetov and Sergei D. Shchebetov, Jan 24 2017

The sequence starts with 1999290307891606810 and continues for another 125 terms (none previously reported, including the first term) each turning into a 119-digit palindrome after 261 steps until the sequence ends with 1999291987030606810. The distance between successive terms in the reported sequence has 9000000 as the greatest common divisor. No further numbers beyond 1999291987030606810 belonging to the same sequence are known, discovered or reported. Moreover, 1999291987030606810 is currently the largest discovered "most delayed palindrome". The sequence was found empirically using computer modeling algorithms.

It is only a conjecture that there are no further terms. - N. J. A. Sloane, Jan 24 2017

			Each term requires exactly 261 steps to turn into a 119-digit palindrome, the last term of A281509, and is separated by some multiples of 9000000 from the adjacent sequence terms.

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

Sergei D. Shchebetov, Table of n, a(n) for n = 1..126
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!

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

A281509 Trajectory of 1999291987030606810 (the largest presently known "most delayed palindrome") under the "Reverse and Add!" operation.

Original entry on oeis.org

1999291987030606810, 2185352294922536801, 3271704589845072613, 6434410079699144336, 12768830049399288682, 41457129443403175403, 71914259877895350817, 143719619755790592734, 581014717313707510075, 1151030424627424920260, 1771324671891665221771, 3542550333873429453542, 5996099577656760005995

Offset: 0

Andrey S. Shchebetov and Sergei D. Shchebetov, Jan 24 2017

1999291987030606810 is the largest of the 126 presently known numbers that require exactly 261 steps to turn into a palindrome (see A281508). It is also the largest discovered "most delayed palindrome". The sequence reaches a 119-digit palindrome after 261 steps (see b-file). The number was obtained empirically using computer algorithms and was not reported before.

			a(1) = 1999291987030606810 + 186060307891929991 = 2185352294922536801.

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

Sergei D. Shchebetov, Table of n, a(n) for n = 0..261
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!

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

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

a(n) = A281507(n) for n>0. - R. J. Mathar, Jan 27 2017

A326414 Numbers which require exactly 288 'Reverse and Add' steps to reach a palindrome.

Original entry on oeis.org

12000700000025339936491, 12000700001015339936491, 12000700002005339936491, 12000700010024339936491, 12000700011014339936491, 12000700012004339936491, 12000700020023339936491, 12000700021013339936491, 12000700022003339936491, 12000700030022339936491

Offset: 1

Andrey S. Shchebetov and Sergei D. Shchebetov, Oct 18 2019

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

Sergei D. Shchebetov, Table of n, a(n) for n = 1..10000
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, 19353600 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!

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

Each term requires exactly 288 steps to turn into a 142-digit palindrome.

Deleted an erroneous comment that said that the sequence was finite. - N. J. A. Sloane, Jun 23 2022

A286481 Numbers which require exactly 260 'Reverse and Add' steps to reach a palindrome.

Original entry on oeis.org

1003062289999939142, 1003062299899939142, 1003062389989939142, 1003062399889939142, 1003062489979939142, 1003062499879939142, 1003062589969939142, 1003062599869939142, 1003062689959939142, 1003062699859939142, 1003062789949939142, 1003062799849939142, 1003062889939939142, 1003062899839939142, 1003062989929939142, 1003062999829939142

Offset: 1

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

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.

			a(1) = 1003062289999939142 + 2419399999822603001 = 3422462289822542143

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

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!

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

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

A353185 Numbers which require exactly 289 'Reverse and Add' steps to reach a palindrome.

Original entry on oeis.org

10037000230509917799950, 10037000240508917799950, 10037000250507917799950, 10037000260506917799950, 10037000270505917799950, 10037000280504917799950, 10037000290503917799950, 10037000330509817799950, 10037000340508817799950

Offset: 1

Andrey S. Shchebetov and Sergei D. Shchebetov, Apr 29 2022

The sequence starts with 10037000230509917799950, ends with 15999771990503200073000 and contains 9031680 terms known at present, including 13968441660506503386020 and 13568441660506503386420 discovered by Anton Stefanov on January 5, 2021.

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

Sergei D. Shchebetov, Table of n, a(n) for n = 1..10000
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, 9031680 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!

A023109, A033672, A065198, A065199, A065320, A065321, A065322, A065323, A065324, A065325, A065326, A065327, A070743, A072216, A072217, A072218, A281301, A281390, A281506, A281507, A326414.

Each term requires exactly 289 steps to turn into a 142-digit palindrome.

A320516 Palindromic wing primes that are also Lychrel candidates.

Original entry on oeis.org

7774777, 777767777, 77777677777, 99999199999, 1111118111111, 7777774777777, 111111181111111, 333333373333333, 77777777677777777, 99999999299999999, 9999999992999999999, 33333333333733333333333, 77777777777677777777777, 333333333333373333333333333

Offset: 1

Robert James Liguori, Oct 29 2018

Lychrel candidates are natural numbers that seem unable to form a palindrome through the iterative process of repeatedly reversing its digits and adding the resulting numbers.

On January 23, 2017 a Russian schoolboy, Andrey S. Shchebetov, announced on his web site that he had found a sequence of the first 126 numbers (125 of them never reported before) that take exactly 261 steps to reach a 119-digit palindrome. That sequence was published in the OEIS as A281506. The trajectory of the last number of that sequence, 1186061987030929990, under the "Reverse and Add!" operation was published separately in the OEIS as A281507.

Robert Liguori, Github project SequencePier

Cf. A077798, A000040, A023108, A281506, A281507.

Seven terms inserted by Jon E. Schoenfield, Oct 31 2018

a(14) from Jon E. Schoenfield, Nov 01 2018

cp's OEIS Frontend

A281507 Trajectory of 1186061987030929990 under the "Reverse and Add!" operation.

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A281508 Numbers requiring exactly 261 'Reverse and Add' steps to reach a palindrome.

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A281509 Trajectory of 1999291987030606810 (the largest presently known "most delayed palindrome") under the "Reverse and Add!" operation.

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A326414 Numbers which require exactly 288 'Reverse and Add' steps to reach a palindrome.

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A286481 Numbers which require exactly 260 'Reverse and Add' steps to reach a palindrome.

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A353185 Numbers which require exactly 289 'Reverse and Add' steps to reach a palindrome.

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A320516 Palindromic wing primes that are also Lychrel candidates.

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