A091680 -id:A091680 - cp's OEIS frontend

A091677 a(n) = smallest non-palindromic k such that the base-4 Reverse and Add! trajectory of k is palindrome-free and joins the trajectory of A091675(n).

469892287, 318, 68346, 66349, 269237759, 272353, 110333, 1082314, 4279, 3903, 1049659, 290, 1210, 4334, 275436, 4199, 73784, 2082046, 5046, 4212653, 1052467, 4768988414, 1073998008, 1051069, 1058784, 719, 795, 799, 265038, 119810013

Offset: 1

Klaus Brockhaus, Jan 28 2004

a(1), a(5), a(22), a(23) and a(30) are conjectural; it is not yet ensured that they are minimal.
a(n) >= A091675(n); a(n) = A091675(n) iff the trajectory of A091675(n) is palindrome-free, i.e., A091675(n) is also a term of A075421.
a(n) determines a 1-1-mapping from the terms of A091675 to the terms of A075421, the inverse of the mapping determined by A091676.
The 1-1 property of the mapping depends on the conjecture that the base-4 Reverse and Add! trajectory of each term of A091675 contains only a finite number of palindromes (cf. A091680).
Base-4 analog of A089494.

			A091675(2) = 3, the trajectory of 3 joins the trajectory of 318 = A075421(2) at 20966400, so a(2) = 318. A091675(4) = 22, the trajectory of 22 joins the trajectory of 66349 = A075421(130) at 600785, so a(4) = 66349.

Index entries for sequences related to Reverse and Add!

Cf. A075421, A091675, A091676, A091680, A089494.

A092215 Smallest number whose base-2 Reverse and Add! trajectory (presumably) contains exactly n base-2 palindromes, or -1 if there is no such number.

Original entry on oeis.org

22, 30, 10, 4, 6, 2, 1, 132, 314, 403, 259, 2048, -1, -1, -1, -1

Offset: 0

Klaus Brockhaus, Feb 25 2004

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).

			a(4) = 6 since the trajectory of 6 contains the four palindromes 9, 27, 255, 765 (1001, 11011, 11111111, 1011111101 in base 2) and at 48960 joins the trajectory of 22 = A075252(1) and the trajectories of 1 (A035522), 2, 3, 4, 5 contain resp. 6, 5, 5, 3, 3 palindromes.

Index entries for sequences related to Reverse and Add!

Cf. A035522, A006995, A075252, A077594, A091680.

cp's OEIS Frontend

A091677 a(n) = smallest non-palindromic k such that the base-4 Reverse and Add! trajectory of k is palindrome-free and joins the trajectory of A091675(n).

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