proposed

approved

editing

proposed

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.

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.

approved

editing

_Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), _, Nov 20 2003

<a href="/Sindx_index/Res.html#RAA">Index entries for sequences related to Reverse and Add!</a>

<a href="/Sindx_Res.html#RAA">Index entries for sequences related to Reverse and Add!</a>

nonn,base,new

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.

<a href="http://www.research.att.com/~njas/sequences/Sindx_Res.html#RAA">Index entries for sequences related to Reverse and Add!</a>

nonn,base,new

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

nonn,base,new

There are (presumably) eleven palindromes in the Reverse and Add! trajectory of n.

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

1,2

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.

<a href="http://www.research.att.com/~njas/sequences/Sindx_Res.html#RAA">Index entries for sequences related to Reverse and Add!</a>

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.

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

nonn,base

Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Nov 20 2003

approved