A307095 Let K_n = prefix of length n of Kolakoski sequence A000002; a(n) is the length of the longest palindromic suffix of K_n.

1, 1, 2, 4, 2, 4, 3, 3, 2, 4, 6, 5, 7, 2, 4, 3, 5, 7, 9, 11, 13, 3, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 6, 3, 2, 4, 6, 5, 7, 2, 4, 3, 3, 2, 4, 6, 8, 10, 12, 6, 5, 7, 2, 4, 3, 5, 7, 9, 11, 13, 3, 2, 4, 6, 5, 7, 2, 4, 3, 5, 7, 6, 3, 2, 4, 6, 8, 10, 12, 2, 4

Offset: 1

Author

Rémy Sigrist, Jun 04 2019

Keywords

• nonn

Examples

			The first terms, alongside K_n with longest palindromic suffix in parentheses, are:
  n   a(n)  K_n
  --  ----  ------------------
   1     1  (1)
   2     1  1(2)
   3     2  1(22)
   4     4  (1221)
   5     2  122(11)
   6     4  12(2112)
   7     3  1221(121)
   8     3  12211(212)
   9     2  1221121(22)
  10     4  122112(1221)
  11     6  12211(212212)
  12     5  1221121(22122)
  13     7  122112(1221221)
  14     2  122112122122(11)
  15     4  12211212212(2112)
  16     3  1221121221221(121)
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..10000
• Rémy Sigrist, PARI program for A307095

Crossrefs

See A220080 for a similar sequence.

Cf. A000002.

Programs

PARI

See Links section.

Formula

a(n+1) <= a(n) + 2.