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

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

Offset: 1

Author

Klaus Brockhaus, Nov 20 2003

Keywords

• nonn
• base

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

• Index entries for sequences related to Reverse and Add!

Crossrefs

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