cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A090072 Numbers n such that there are (presumably) eleven palindromes in the Reverse and Add! trajectory of n.

Original entry on oeis.org

1, 20000, 20002, 1000000, 1000001, 10000000, 10000001
Offset: 1

Views

Author

Klaus Brockhaus, Nov 20 2003

Keywords

Comments

Additional terms (cf. A090075) are 100000000, 100000001, 100010001, 1000000000, 1000000001, 10000000000, 10000000001, 100000000000, 100000000001, 1000000000000, 1000000000001, 1000001000001, 1000100010001, but it is not yet ascertained that they are consecutive.
For all terms given above each palindrome is reached from the preceding one or from the start in at most 35 steps; after the presumably last one no further palindrome is reached in 5000 steps.
Only two numbers are known whose Reverse and Add trajectory contains twelve palindromes: 10000 and 10001. It is conjectured that these are the only such numbers and it has been conjectured before (cf. A077594) that no Reverse and Add trajectory contains more than twelve palindromes.

Examples

			The trajectory of 1 begins 1, 2, 4, 8, 16, 77, 154, 605, 1111, 2222, 4444, 8888, 17776, 85547, 160105, 661166, 1322332, 3654563, 7309126, ...; at 7309126 it joins the (presumably) palindrome-free trajectory of A063048(7) = 10577, hence 1, 2, 4, 8, 77, 1111, 2222, 4444, 8888, 661166 and 3654563 are the eleven palindromes in the trajectory of 1 and 1 is a term.

Links

Crossrefs

Cf. A023108, A023109, A065001, A070742, A077594, A090075.

A090074 (Presumed) last palindrome in the Reverse and Add! trajectory of 10^n.

Original entry on oeis.org

3654563, 678736545637876, 663305503366, 663787366, 88352682264077046228625388, 365468864563, 3654566654563, 36545633654563, 365456303654563, 3654563003654563, 36545630003654563, 365456300003654563
Offset: 0

Views

Author

Klaus Brockhaus, Nov 20 2003

Keywords

Comments

No further palindrome is reached in 5000 steps.
The number of palindromes in the Reverse and Add! trajectory of 10^n is given in A090075.

Links

Crossrefs

Cf. A065001, A070742, A077594, A090069, A090070, A090071, A090072, A090075.

Formula

a(n) = 3654563*10^(n) + 3654563 for n > 5.
Showing 1-2 of 2 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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