cp's OEIS Frontend

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.

%I A098894 #8 Jul 14 2022 22:54:50
%S A098894 1,2,5,8,15,22,39,56,97,138,237,336,575,814,1391,1968,3361,4754,8117,
%T A098894 11480,19599,27718,47319,66920,114241,161562,275805,390048,665855,
%U A098894 941662,1607519,2273376,3880897,5488418,9369317
%N 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.
%C A098894 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.
%C A098894 Conjecture: partial sums of A152113. - _Sean A. Irvine_, Jul 14 2022
%e A098894 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,...
%Y A098894 Cf. A034182, A082766.
%K A098894 nonn
%O A098894 1,2
%A A098894 _John W. Layman_, Nov 04 2004