A098894 Values of k such that {s(1),...,s(k)} is a palindrome, where {s(1),s(2),...} is the fixed point of the substitutions 0->1 and 1->110.

1, 2, 5, 8, 15, 22, 39, 56, 97, 138, 237, 336, 575, 814, 1391, 1968, 3361, 4754, 8117, 11480, 19599, 27718, 47319, 66920, 114241, 161562, 275805, 390048, 665855, 941662, 1607519, 2273376, 3880897, 5488418, 9369317

Offset: 1

Author

John W. Layman, Nov 04 2004

Keywords

• nonn

Comments

Superseeker suggests: (1) o.g.f. (1+x+x^2+x^3)/(1+2x-2x^2-x^3+x^4+x^5), (2) terms of odd index {1,5,15,39,...} give A034182 and (3) {a(n)+2} gives A082766, except for several initial terms.

Conjecture: partial sums of A152113. - Sean A. Irvine, Jul 14 2022

Examples

			Start with 1 and iterate the substitutions 0->1, 1->110 to get 1, 110, 1101101, 11011011101101110, 11011011101101110110110111011011101101101,... The initial terms from the beginning to the single quotes form palindromes: 1'1'011'011'1011011'1011011',..., of lengths 1,2,5,8,15,22,...
		

Crossrefs

Cf. A034182, A082766.