A179835Smallest k > 0 such that prime(n-k) + prime(n+k) = 2*prime(n), or 0 if there is no such k.

0, 0, 1, 0, 2, 2, 2, 0, 0, 3, 3, 6, 3, 0, 0, 1, …

The first 4 terms appear at position 9,984.

…3699989225695968815920560010165525637567856672279661…
position 9,984
termsstringfirst positionoccurrences
103299,993,942
20030710,004,524
30013601,000,758
400109,984100,004
50010228,18110,101
60010221,037,932991
700102227,904,59294
80010222063,919,77910
9001022200185,259,0801
100010222003185,259,0801
1100102220033185,259,0801
12001022200336185,259,0801

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