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a(n) = 2*A111619/n.
2

%I #3 Mar 30 2012 17:31:16

%S 1,1,1,1,2,1,2,1,1,1,1,1,2,1,2,1,1,1,2,1,2,1,2,2,2,2,1,2,1,1,1,1,2,1,

%T 2,2,2,2,2,1,2,2,2,2,2,2,2,1,1,2,1,2,2,2,2,2,2,1,2,2,2,2,2,1,1,1,2,1,

%U 1,1,2,1

%N a(n) = 2*A111619/n.

%C A sequence of just 1's and 2's.

%C 2n divided A111619 is: 2,2,2,2,1,2,1,2,2,2,2,2,1,2,1,2,2,2,1,2,1,2,1,1,1,1,2,1,2,2,2,2,1,2,1,1,1,1,1,2,1,1,1,1,1,1,1,2,2,1,2,1,1,1,1,1,1,2,1,1,1,1,1,2,2,2,1,2,2,2,1,2,..., Table[ n/g[n, n - 1], {n, 2, 144, 2}].

%C A111620(n) plus the n-th entry immediately above = 3.

%t f[n_] := f[n] = Block[{a}, a[0] = 1; a[l_] := a[l] = Block[{k = 1, s = Sum[ a[i]*x^i, {i, 0, l - 1}]}, While[ IntegerQ[ Last[ CoefficientList[ Series[(s + k*x^l)^(1/n), {x, 0, l}], x]]] != True, k++ ]; k]; Table[ a[j], {j, 0, 144}]]; g[n_, m_] := f[n][[m]]; Table[ 3 - n/g[n, n - 1], {n, 2, 144, 2}] (* or *) Table[ 2*g[n, n - 1]/n, {n, 2, 144, 2}]

%Y Cf. A111618.

%K nonn

%O 1,5

%A _Robert G. Wilson v_, Aug 03 2005