cp's OEIS Frontend

Conjecture: Only one digit needs to be inserted between each pair of digits of a(n-1) to get a(n); i.e., a(n) contains exactly 2n-1 digits for n > 1.

The conjecture above is false: a(5)=10000000000060571 has 17 digits instead of 2*5-1=9. A refined conjecture is: a(n) contains exactly 2^(n-1) + 1 digits for all n>0. This follows trivially by induction from the initial conjecture (above) of only one digit needed between each pair, and the fact that we start with 11, a 2-digit number, and holds true at least till a(12). - Julio Cesar Hernandez-Castro, Jul 05 2011

Conjecture: Only one digit needs to be inserted between each pair of digits of a(n-1) to get a(n); i.e., a(n) contains exactly 2n-1 digits for n > 1.

The conjecture above is false: a(4) = 100000963 has 9 digits instead of 2*4 - 1 = 7. A refined conjecture is: a(n) contains exactly 2^(n-1) + 1 digits for all n > 0. This follows trivially by induction from the initial above conjecture of only one digit needed between each pair, and the fact that we start with 13, a 2-digit number, and holds true at least till a(12). - Julio Cesar Hernandez-Castro, Jul 06 2011

Conjecture: Only one digit needs to be inserted between each pair of digits of a(n-1) to get a(n); i.e. a(n) contains exactly 2n-1 digits for n > 1.

The conjecture above is false: a(5) = 10000000000003037 has 17 digits instead of 2*5 - 1 = 9. A refined conjecture is: a(n) contains exactly 2^(n-1) + 1 digits for all n > 0. This follows trivially by induction from the initial conjecture above of only one digit needed between each pair, and the fact that we start with 17, a 2-digit number, and holds true at least till a(12).