A000045Fibonacci numbers: F(n) = F(n-1) + F(n-2) with F(0) = 0 and F(1) = 1.

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, …

The first 3 terms appear at position 361.

…5358979323846264338327950288419716939937510582097…

position 32

…59408128481117450284102701938521105559644622948954…

position 167

…254091715364367892590360011330530548820466521384146…

position 361

…5135751782966645477917450112996148903046399471329621…

position 4,448

…70563872931748723320837601123029911367938627089438799…

position 7,143

…671314915262504417545271011235786801298936828493391396…

position 161,562

…3858708321285776638719120112358756831460809564596886992…

position 4,253,057

terms	string	first position	occurrences
1	0	32	99,993,942
2	01	167	9,998,250
3	011	361	1,001,188
4	0112	4,448	100,300
5	01123	7,143	10,026
6	011235	161,562	979
7	0112358	4,253,057	86
8	011235813	not within 1,000,000,000	0
9	01123581321	not within 1,000,000,000	0

Searched the first 1,000,000,000 digits. Strings longer than 12 digits are not indexed.