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a(n) = minimal number of consecutive integers required which when summed make n.
12

%I #8 Apr 17 2023 12:22:44

%S 0,2,0,2,0,2,3,2,0,2,4,2,3,2,4,2,0,2,3,2,5,2,4,2,3,2,4,2,7,2,3,2,0,2,

%T 4,2,3,2,4,2,5,2,3,2,8,2,4,2,3,2,4,2,8,2,3,2,7,2,4,2,3,2,4,2,0,2,3,2,

%U 8,2,4,2,3,2,4,2,8,2,3,2,5,2,4,2,3,2,4,2,11,2,3,2,8,2,4,2,3,2,4,2,5,2,3,2

%N a(n) = minimal number of consecutive integers required which when summed make n.

%C Zeros occur where no number of consecutive integers can be summed to make n; This only happens where n is an even power of two, or zero itself.

%C Entries where this sequence is nonzero are in A138591.

%H Ray Chandler, <a href="/A163169/b163169.txt">Table of n, a(n) for n = 0..10000</a>

%e 20 = 2 + 3 + 4 + 5 + 6; No shorter sequence of consecutive integers sums to 20 and so a(20) = the number of elements in {2,3,4,5,6} = 5.

%e 15 = 4 + 5 + 6, but also 15 = 7 + 8, so a(15) = 2, since this is the minimum.

%Y Cf. A138591, A057716.

%K easy,nonn

%O 0,2

%A _Carl R. White_, Jul 22 2009