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A379797 In A377091, each block of consecutive terms of the same sign is followed by a jump of magnitude +-s^2 for some integer s>0 to a term of the opposite sign; sequence lists the successive values of s.

%I A379797 #24 Mar 30 2025 16:21:52
%S A379797 2,2,3,3,4,5,5,6,6,7,7,8,9,9,10,10,11,11,12,12,13,14,14,15,15,16,16,
%T A379797 17,17,18,18,19,20,20,21,21,22,22,23,23,24,24,25,26,26,27,27,28,28,29,
%U A379797 29,30,30,31,31,31,32,32,32,33,33,33,33,34,34,35,35,35,36,36,37,37,37,38,38,38,39,39,39,39,40,40,40,40,41,41
%N A379797 In A377091, each block of consecutive terms of the same sign is followed by a jump of magnitude +-s^2 for some integer s>0 to a term of the opposite sign; sequence lists the successive values of s.
%H A379797 N. J. A. Sloane, <a href="/A379797/b379797.txt">Table of n, a(n) for n = 1..1024</a>
%F A379797 If n = 2*k-1, k>=1, then a(n) = sqrt{A379791(k)-A379793(k)}; if n = 2k, k>=1, then a(n) = sqrt{A379789(k+1)-A379066(k)}.
%e A379797 The initial terms of A377091 are
%e A379797    0, 1, 2, -2, -1, 3, 4, 5, -4, -3, 6, 7, 8, -8, -7, -6, -5, -9, -10, -11, -12, 13, 9, 10, 11, 12, -13, -14
%e A379797 and the jumps we are talking about are
%e A379797    __________4______4_________9______9________16__________________________________25__________________25_____
%e A379797 whose square roots are 2, 2, 3, 3, 4, 5, 5, ... which is the current sequence. - _N. J. A. Sloane_, Mar 30 2025
%Y A379797 Cf. A377091, A379066, A379788-A379794, A380837.
%Y A379797 See A379798 for first differences.
%K A379797 nonn
%O A379797 1,1
%A A379797 _N. J. A. Sloane_, Jan 18 2025