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.

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, 17, 17, 18, 18, 19, 20, 20, 21, 21, 22, 22, 23, 23, 24, 24, 25, 26, 26, 27, 27, 28, 28, 29, 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

Offset: 1

Author

N. J. A. Sloane, Jan 18 2025

Keywords

• nonn

Examples

			The initial terms of A377091 are
   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
and the jumps we are talking about are
   __________4______4_________9______9________16__________________________________25__________________25_____
whose square roots are 2, 2, 3, 3, 4, 5, 5, ... which is the current sequence. - _N. J. A. Sloane_, Mar 30 2025
		

Links

• N. J. A. Sloane, Table of n, a(n) for n = 1..1024

Crossrefs

Cf. A377091, A379066, A379788-A379794, A380837.

See A379798 for first differences.

Formula

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)}.