A111619 -id:A111619 - cp's OEIS frontend

A111620 a(n) = 2*A111619/n.

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, 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, 1, 1, 2, 1

Offset: 1

Robert G. Wilson v, Aug 03 2005

nonn

A sequence of just 1's and 2's.
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}].
A111620(n) plus the n-th entry immediately above = 3.

Cf. A111618.

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}]

A111618 First lower diagonal of A109626.

Original entry on oeis.org

1, 3, 2, 5, 3, 7, 4, 9, 10, 11, 6, 13, 14, 15, 8, 17, 9, 19, 10, 21, 11, 23, 12, 25, 26, 27, 14, 29, 30, 31, 16, 33, 17, 35, 18, 37, 38, 39, 20, 41, 42, 43, 22, 45, 46, 47, 48, 49, 50, 51, 52, 53, 27, 55, 56, 57, 29, 59, 30, 61, 31, 63, 32, 65, 66, 67, 34, 69, 70, 71, 72, 73, 74

Offset: 2

Paul D. Hanna and Robert G. Wilson v, Aug 01 2005

nonn

The odd-indexed bisection is a(2n+1)=2n+1.

The even-indexed bisection: A111619.

Cf. A109626, A111619, A111620.

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, 80}]]; g[n_, m_] := f[n][[m]]; Table[ g[n, n - 1], {n, 2, 74}]

cp's OEIS Frontend

A111620 a(n) = 2*A111619/n.

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