A334194a(n) = n - d1*d2, where d1, d2 are the distances from n to the previous and the next prime number respectively.

1, 3, 1, 5, -1, 5, 5, 7, 3, 11, 5, 11, 11, 13, 9, 17, …

This sequence has negative terms. Minus signs are dropped before searching.

The first 9 terms appear at position 758,052,404.

…777331502411331198034288131515573964507318220072213605359…
position 758,052,404
termsstringfirst positionoccurrences
11199,997,334
2131109,998,738
31311,0961,001,090
413151,096100,103
5131511,0969,890
61315151,096970
713151551,09692
8131515571,09611
9131515573758,052,4041
1013151557311not within 1,000,000,0000
11131515573115not within 1,000,000,0000

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