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A386525 a(n) is the least k such that at least n terms of A063655 starting from index k are strictly decreasing.

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%I A386525 #11 Aug 15 2025 00:06:13
%S A386525 1,5,13,37,122,3004,26283,53411,109453,4117156,16831081
%N A386525 a(n) is the least k such that at least n terms of A063655 starting from index k are strictly decreasing.
%C A386525 Lai and Reinfeld conjecture that the sequence is infinite.
%H A386525 H. Lai and M. Reinfeld, <a href="http://girlsangle.org/page/bulletin-archive/GABv18n05E.pdf">An Introduction to LR Numbers</a>, Girls' Angle Bulletin, Vol. 18, No. 5 (2025), 11-15.
%e A386525 The first 40 values of A063655 are: 2, 3, 4, 4, 6, 5, 8, 6, 6, 7, 12, 7, 14, 9, 8, 8, 18, 9, 20, 9, 10, 13, 24, 10, 10, 15, 12, 11, 30, 11, 32, 12, 14, 19, 12, 12, 38, 21, 16, and 13. Because the 37th term is the first of 4 strictly decreasing values and there is not previous occurrence of four decreasing values, a(3) = 37.
%Y A386525 Cf. A063655.
%K A386525 nonn,more
%O A386525 1,2
%A A386525 _Richard S. Chang_, Jul 24 2025
%E A386525 a(11) from _Sean A. Irvine_, Aug 10 2025