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 A307325 a(n) is the smallest number k for which prime(k+1) - prime(k) is greater than n. 0
 2, 4, 4, 9, 9, 24, 24, 30, 30, 30, 30, 30, 30, 99, 99, 99, 99, 154, 154, 189, 189, 217, 217, 217, 217, 217, 217, 217, 217, 217, 217, 217, 217, 1183, 1183, 1831, 1831, 1831, 1831, 1831, 1831, 1831, 1831, 2225, 2225, 2225, 2225, 2225, 2225, 2225, 2225, 3385, 3385, 3385, 3385 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS For any n there is an infinity of numbers m for which prime(m+1) - prime(m) is greater than n. It appears that the sequence of lengths of successive runs is equal to A053695. - Marc Bofill Janer, May 21 2019 REFERENCES Laurențiu Panaitopol, Dinu Șerbănescu, Number theory and combinatorial problems for juniors, Ed.Gil, Zalău, (2003), ch. 1, p.7, pr. 25. (in Romanian). LINKS Table of n, a(n) for n=1..55. FORMULA a(2*n) = a(2*n+1) = A144309(n+1) for n>=1. - Georg Fischer, Dec 05 2022 EXAMPLE For n = 2, prime(2) - prime(1) = 3 - 2 = 1, prime(3) - prime(2) = 5 - 3 = 2, prime(5) - prime(4) = 11 - 7 = 4, so a(2) = 4. PROG (MATLAB) v=primes(1000000); for u=1:100; ss=1; while and(v(ss+1)-v(ss)<=u, ss

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Last modified September 17 17:26 EDT 2024. Contains 375990 sequences. (Running on oeis4.)