1,3

Construction: start with strings S(1)={1}, S(2)={1,3}, S(3)={1,5}; to obtain S(k) for k>3, concatenate all previous strings excluding S(k-1), then replace the last number L in this resulting string with {4L-(-1)^k}. This sequence is the limit of S(k) as k grows, generating strings with Fibonacci growth: {1,1,11}, {1,1,3,1,21}, {1,1,3,1,5,1,1,43}, {1,1,3,1,5,1,1,11,1,1,3,1,85}, ...

For n>0, a(F(n))=A001045(n), where F(n) is the n-th Fibonacci number with F(1)=1, F(2)=2.

To generate string S(4) at k=4: concatenate {S(1),S(2)} = {1, 1,3}, then replace the last number L=3 by 4*L-1=11 to obtain S(4)={1,1,11}.

At k=5: concatenate {S(1),S(2),S(3)} = {1, 1,3, 1,5}, then replace the last number L=5 by 4*L+1=21 to obtain S(5)={1,1,3,1,21}.

Cf. A006013, A001045, A085405, A022340 (positions of ones).

Sequence in context: A002945 A093423 A134700 this_sequence A016475 A037227 A056753

Adjacent sequences: A085404 A085405 A085406 this_sequence A085408 A085409 A085410

nonn

Paul D. Hanna (pauldhanna(AT)juno.com), Jun 29 2003