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 A359440 A measure of the extent of reflective symmetry in the pattern of primes around each prime gap: a(n) is the largest k such that prime(n-j) + prime(n+1+j) has the same value for each j in 0..k. 9
 0, 0, 0, 1, 2, 2, 1, 0, 0, 4, 0, 0, 2, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 2, 1, 0, 1, 0, 0, 0, 2, 0, 0, 0, 5, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 COMMENTS If the prime gaps above and below a prime p have the same length, p is called a balanced prime (see A006562). Likewise, if the prime gaps above and below the n-th prime gap have the same length, this gap might be called a balanced prime gap. These gaps correspond to nonzero terms a(n). Similarly, if a(n) >= 2, the n-th prime gap is the equivalent of a doubly balanced prime (A051795), and so on. - Peter Munn, Jan 08 2023 LINKS Table of n, a(n) for n=1..87. FORMULA a(n) = min( {n-1} U {k : 0 <= k <= n-2 and prime(n-k-1) + prime(n+k+2) <> prime(n) + prime(n+1)} ). - Peter Munn, Jan 08 2023 EXAMPLE For n = 1, prime(1) + prime(2) = 2 + 3 = 5; "prime(0)" does not exist, so a(1) = 0. For n = 4: j = 0: prime(4) + prime(5) = 7 + 11 = 18; j = 1: prime(3) + prime(6) = 5 + 13 = 18; j = 2: prime(2) + prime(7) = 3 + 17 = 20 != 18, so a(4) = 1. For n = 5: j = 0: prime(5) + prime(6) = 11 + 13 = 24; j = 1: prime(4) + prime(7) = 7 + 17 = 24; j = 2: prime(3) + prime(8) = 5 + 19 = 24; j = 3: prime(2) + prime(9) = 3 + 23 = 26 != 24, so a(5) = 2. PROG (Python) import sympy offset = 1 N = 100 l = [] for n in range(offset, N+1): j = 0 first_sum = sympy.prime(n-j)+sympy.prime(n+j+1) while (n-j) > 1: j += 1 sum = sympy.prime(n-j)+sympy.prime(n+j+1) if sum != first_sum: break l.append(max(0, j-1)) print(l) CROSSREFS Cf. A000040, A006562, A051795, A055381, A081235. Sequence in context: A352988 A334493 A074080 * A347687 A287331 A179769 Adjacent sequences: A359437 A359438 A359439 * A359441 A359442 A359443 KEYWORD nonn AUTHOR Alexandre Herrera, Jan 01 2023 EXTENSIONS Introductory phrase added to name by Peter Munn, Jan 08 2023 STATUS approved

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Last modified November 29 00:31 EST 2023. Contains 367422 sequences. (Running on oeis4.)