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 term appear at position 1.

1415926535897932384626433…
position 1
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.