A000079Powers of 2: a(n) = 2^n.

1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, …

The first 6 terms appear at position 20,467,663.

…05604972448486963317511612481632969480364989854158012815…
position 20,467,663
termsstringfirst positionoccurrences
11199,997,334
21214810,000,708
31241,080999,126
4124818,38199,799
5124816243,587960
61248163220,467,66318
71248163264not within 1,000,000,0000

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