cp's OEIS Frontend

a(3), a(14) and a(18) are conjectural; it is not yet ensured that they are minimal.

a(n) >= A070788(n); a(n) = A070788(n) iff the trajectory of A070788(n) is palindrome-free, i.e. A070788(n) is also a term of A063048.

a(n) determines a 1-1-mapping from the terms of A070788 to the terms of A063048, the inverse of the mapping determined by A089493. Terms > 2*10^6 were ascertained with the aid of W. VanLandingham's list of Lychrel numbers.

The 1-1 property of the mapping depends on the conjecture that the Reverse and Add! trajectory of each term of A070788 contains only a finite number of palindromes (cf. A077594). - Klaus Brockhaus, Dec 09 2003

For terms <= 5000 each palindrome is reached from the preceding one or from the start in at most 15 steps; after the presumably last one no further palindrome is reached in 2000 steps.

For terms < 5000000 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 2000 steps.

Additional terms are 20000000, 20000002, 200000000, 200000002, 2000000000, 2000000002, 10000000004, 10000100001, 20000000000, 20000000002, 20000000003, 30000000002, 40000000001, 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.

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.

The absolute maximum 12 at n = 4 and a(n) = 11 for n > 5 support the conjecture (cf. A077594) that there is no positive integer whose trajectory contains more than twelve palindromes.

The last palindrome in the Reverse and Add! trajectory of 10^n is given in A090074.

Conjecture 1: For each k > 0 the trajectory of k eventually leads to a term in the trajectory of some j which belongs to A075421, i.e., whose trajectory (presumably) never leads to a palindrome. Conjecture 2: There is no k > 0 such that the trajectory of k contains more than twelve palindromes, i.e., a(n) = -1 for n > 12.

Base-4 analog of A077594.

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.

Conjecture 1: For each k > 0 the trajectory of k eventually leads to a term in the trajectory of some j which belongs to A075252, i.e., whose trajectory (presumably) never leads to a palindrome. Conjecture 2: There is no k > 0 such that the trajectory of k contains more than eleven base 2 palindromes, i.e., a(n) = -1 for n > 11.

Base-2 analog of A077594 (base 10) and A091680 (base 4).