150,000-Term Computational Audit of a Neighboring-Prime Linear Form: OEIS A094105 and the APC Infinitude Conjecture

This computational research note studies the neighboring-prime form p(k) + 2p(k+1), whose prime values were recorded by Giovanni Teofilatto as OEIS A094105 in 2004. Let p(1) = 3, p(2) = 5, and so forth denote the consecutive odd primes. In the indexing used for the audit, F(i) = 2p(i) + p(i-1) for i greater than or equal to 2. After setting k = i-1, this is equivalent to p(k) + 2p(k+1). The paper explicitly formulates the associated APC infinitude conjecture: there are infinitely many indices k for which p(k) + 2p(k+1) is prime. A corrected, frozen computational audit of 150,000 consecutive prime pairs found 15,226 prime outputs and 134,774 composite outputs, giving an observed prime-output rate of 10.1507 percent. Unlike a success-only sequence table, the audit preserves the complete tested range and its failures. It also reports 1,000-term block statistics, longest prime and composite runs, a simple prime-density comparison, companion and control constructions, a fixed-seed symbolic diagnostic, exact computational endpoints, and SHA-256 reproducibility records. Searches of the cited sequence records and exact-form literature conducted for this revision did not locate an earlier source explicitly asserting that the form is prime for infinitely many indices. This is a qualified literature-search result, not a guarantee that no earlier statement exists. This paper does not claim discovery of the underlying sequence or a proof of infinitude. Historical credit for the recorded sequence is given to Giovanni Teofilatto and the other OEIS contributors cited in the paper. The finite computation is consistent with continued occurrence but does not establish infinitude or an exceptional prime-producing density.