A089494 -id:A089494 - cp's OEIS frontend

A089493 a(n) = smallest k such that the Reverse and Add! trajectory of A063048(n) joins the trajectory of k.

196, 879, 106, 1077, 10553, 111, 1, 10583, 10022, 10071, 10331, 10128, 10210, 10132, 10278, 113, 10746, 10748, 1057, 10122, 10123, 10248, 10337, 10220, 10204, 10212, 10969, 10437, 10983, 10222, 10183, 12898, 128, 10119, 13694, 10036, 10292, 10173

Offset: 1

Klaus Brockhaus, Nov 04 2003

a(n) <= A063048(n); a(n) = A063048(n) iff the trajectory of A063048(n) does not join the trajectory of any smaller number, i.e. A063048(n) is also a term of A070788.

a(n) determines a 1-1-mapping from the terms of A063048 to the terms of A070788. For the inverse mapping cf. A089494.

			A063048(3) = 1997, the trajectory of 1997 joins the trajectory of 106 = A070788(8) at 97768, so a(3) = 106. A063048(7) = 10577, the trajectory of 10577 joins the trajectory of 1 = A070788(1) at 7309126, so a(7) = 1.

Index entries for sequences related to Reverse and Add!

Cf. A063048, A070788, A089494.

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).

Original entry on oeis.org

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.

A092212 a(n) = smallest non-palindromic k such that the base-2 Reverse and Add! trajectory of k is palindrome-free and joins the trajectory of A092210(n).

Original entry on oeis.org

26, 65649, 89, 4193, 3599, 775, 68076, 2173

Offset: 1

Klaus Brockhaus, Feb 25 2004

Terms a(9) to a(29) are 205796147 (conjectured), 4402, 16720, 1089448, 442, 537, unknown, 1050177, 1575, 28822, unknown, 40573, 1066, 1587, unknown, unknown, 1081, 1082, 1085, 1115, 4185.
a(n) >= A092210(n); a(n) = A092210(n) iff the trajectory of A092210(n) is palindrome-free, i.e., A092210(n) is also a term of A075252.
a(n) determines a 1-to-1 mapping from the terms of A092210 to the terms of A075252, the inverse of the mapping determined by A092211.
The 1-to-1 property of the mapping depends on the conjecture that the base-2 Reverse and Add! trajectory of each term of A092210 contains only a finite number of palindromes (cf. A092215).
Base-2 analog of A089494 (base 10) and A091677 (base 4).

			A092210(3) = 64, the trajectory of 64 joins the trajectory of 89 at 48480, so a(3) = 89. A092210(5) = 98, the trajectory of 98 joins the trajectory of 3599 = A075252(16) at 401104704, so a(5) = 3599.

Index entries for sequences related to Reverse and Add!

Cf. A075252, A092210, A092211, A092215, A089494, A091677.

limit = 10^3; (* Assumes that there is no palindrome if none is found before "limit" iterations *)
utraj = NestList[# + IntegerReverse[#, 2] &, 1, limit];
A092210 = Flatten@{1, Select[Range[2, 266], (l =
        Length@NestWhileList[# + IntegerReverse[#, 2] &, #, !
            MemberQ[utraj, #] &, 1, limit];
       utraj =
        Union[utraj, NestList[# + IntegerReverse[#, 2] &, #, limit]];
       l == limit + 1) &]};
A092212 = {};
For[i = 1, i <= Length@A092210, i++,
k = A092210[[i]];
itraj = NestList[# + IntegerReverse[#, 2] &, A092210[[i]], limit];
While[ktraj =
   NestWhileList[# + IntegerReverse[#, 2] &,
    k, # != IntegerReverse[#, 2] &, 1, limit];
  PalindromeQ[k] || Length@ktraj != limit + 1 || ! IntersectingQ[itraj, ktraj], k++];
AppendTo[A092212, k]]; A092212 (* Robert Price, Nov 03 2019 *)

a(1) and a(3) corrected by Robert Price, Nov 06 2019

cp's OEIS Frontend

A089493 a(n) = smallest k such that the Reverse and Add! trajectory of A063048(n) joins the trajectory of k.

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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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A092212 a(n) = smallest non-palindromic k such that the base-2 Reverse and Add! trajectory of k is palindrome-free and joins the trajectory of A092210(n).

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