A371905 - OEIS

A371905

Let k = 0 and let A007814(2*n) = m; If m > k then a(n) = k = k + m, otherwise a(n) = k = k - m.

1, 3, 2, 5, 4, 2, 1, 5, 4, 2, 1, 4, 3, 1, 0, 5, 4, 2, 1, 4, 3, 1, 0, 4, 3, 1, 0, 3, 2, 0, 1, 7, 6, 4, 3, 0, 1, 3, 2, 6, 5, 3, 2, 5, 4, 2, 1, 6, 5, 3, 2, 5, 4, 2, 1, 5, 4, 2, 1, 4, 3, 1, 0, 7, 6, 4, 3, 0, 1, 3, 2, 6, 5, 3, 2, 5, 4, 2, 1, 6, 5, 3, 2, 5, 4, 2, 1

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OFFSET

1,2

LINKS

Michael De Vlieger, Table of n, a(n) for n = 1..10000

EXAMPLE

Let f(x) = A007814(x).

a(1) = 1 because k = 0 and f(2*1) = 1; since 0 < 1, a(1) = k = 0 + 1 = 1.

a(2) = 3 because k = 1 and f(2*2) = 2; since 1 < 2, a(2) = k = 1 + 2 = 3.

a(3) = 2 because k = 3 and f(2*3) = 1; since 3 > 2, a(3) = k = 3 - 1 = 2, etc.

MATHEMATICA

nn = 120; k = 0; q = 2; Reap[Do[If[k < #, k += #, k -= #] &@ IntegerExponent[q*n, q]; Sow[k], {n, nn}]][[-1, 1]]