A377351 Lexicographically earliest sequence of positive integers such that the means of consecutive terms are all distinct.
1, 2, 4, 7, 5, 10, 12, 18, 13, 16, 28, 23, 14, 25, 48, 32, 17, 46, 30, 45, 67, 60, 27, 71, 39, 85, 68, 99, 78, 44, 102, 87, 126, 57, 118, 69, 121, 74, 125, 119, 112, 136, 107, 110, 170, 120, 175, 142, 194, 75, 222, 152, 164, 180, 177, 184, 188, 135, 255, 210
Offset: 1
Keywords
Examples
The first terms, alongside the means of consecutive terms ending with a(n), are: n a(n) Corresponding means - ---- ------------------------------------------ 1 1 1 2 2 3/2, 2 3 4 7/3, 3, 4 4 7 7/2, 13/3, 11/2, 7 5 5 19/5, 9/2, 16/3, 6, 5 6 10 29/6, 28/5, 13/2, 22/3, 15/2, 10 7 12 41/7, 20/3, 38/5, 17/2, 9, 11, 12 8 18 59/8, 58/7, 28/3, 52/5, 45/4, 40/3, 15, 18
Links
- Rémy Sigrist, Table of n, a(n) for n = 1..10000
- Rémy Sigrist, C++ program
Programs
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Python
from fractions import Fraction from itertools import count, islice def agen(): # generator of terms alst, means_seen = [1], {1} while True: yield alst[-1] for k in count(1): if k in means_seen: continue mk, failed, sk = {k}, False, k for j in range(1, len(alst)+1): sk += alst[-j] m = Fraction(sk, j+1) if m in means_seen or m in mk: failed = True; break mk.add(m) if not failed: break means_seen |= mk alst.append(k) print(list(islice(agen(), 60))) # Michael S. Branicky, Oct 26 2024, Oct 28 2024
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