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 A370517 a(n) is the largest prime p such that all prime numbers q <= p have distinct length n prime gap sequences. 0
 3, 7, 7, 7, 47, 251, 421, 421, 9769, 9769, 36469, 36469, 36469, 184224493, 2159263321, 13848073963, 33980350373 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Given p(i) the i-th prime number, the gap sequence of length n for prime p(i) is defined as: p(i+1)-p(i), p(i+2)-p(i+1), ..., p(i+n)-p(i+n-1). E.g., the length 3 gap sequence of 7 is [11-7, 13-11, 17-13] is [4, 2, 4]. LINKS Table of n, a(n) for n=1..17. EXAMPLE For n = 5, the largest prime with a distinct gap sequence is 47. For all primes up to and including 47, the length 5 gap sequences are distinct, while the next prime, 53, has a gap sequence equal to 23, namely [6, 2, 6, 4, 2]. PROG (Python) s = set() for p, g in ((w[0][0], tuple(r - q for q, r in w[1:])) for w in sliding_window(pairwise(primes()), n + 1)): if g in s: return p else: s.add(g) CROSSREFS Cf. A001223. Sequence in context: A193016 A349604 A325894 * A176269 A343644 A081522 Adjacent sequences: A370514 A370515 A370516 * A370518 A370519 A370520 KEYWORD nonn,more AUTHOR Leo Vandriel, Feb 21 2024 STATUS approved

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Last modified August 3 19:43 EDT 2024. Contains 374909 sequences. (Running on oeis4.)