A084432 -id:A084432 - cp's OEIS frontend

A373184 G.f. A(x) satisfies A(x) = 1/(1 - x)^2 - 1 + A(x^3).

2, 3, 6, 5, 6, 10, 8, 9, 16, 11, 12, 18, 14, 15, 22, 17, 18, 29, 20, 21, 30, 23, 24, 34, 26, 27, 44, 29, 30, 42, 32, 33, 46, 35, 36, 55, 38, 39, 54, 41, 42, 58, 44, 45, 68, 47, 48, 66, 50, 51, 70, 53, 54, 84, 56, 57, 78, 59, 60, 82, 62, 63, 94, 65, 66, 90, 68, 69, 94, 71, 72, 107, 74, 75, 102, 77, 78, 106, 80, 81

Offset: 1

Seiichi Manyama, May 27 2024

Seiichi Manyama, Table of n, a(n) for n = 1..10000

Cf. A084432, A373185.

Cf. A327625.

def A(k, n)
  ary = [0]
  (1..n).each{|i|
    j = i + 1
    j += ary[i / k] if i % k == 0
    ary << j
  }
  ary[1..-1]
end
p A(3, 80)

a(3*n+1) = 3*n+2, a(3*n+2) = 3*n+3 and a(3*n+3) = 3*n+4 + a(n+1) for n >= 0.

G.f.: A(x) = Sum_{k>=0} (1/(1 - x^(3^k))^2 - 1).

A373185 G.f. A(x) satisfies A(x) = 1/(1 - x)^2 - 1 + A(x^4).

Original entry on oeis.org

2, 3, 4, 7, 6, 7, 8, 12, 10, 11, 12, 17, 14, 15, 16, 24, 18, 19, 20, 27, 22, 23, 24, 32, 26, 27, 28, 37, 30, 31, 32, 45, 34, 35, 36, 47, 38, 39, 40, 52, 42, 43, 44, 57, 46, 47, 48, 66, 50, 51, 52, 67, 54, 55, 56, 72, 58, 59, 60, 77, 62, 63, 64, 89, 66, 67, 68, 87, 70, 71, 72, 92, 74, 75, 76, 97, 78, 79, 80, 108, 82, 83, 84, 107

Offset: 1

Seiichi Manyama, May 27 2024

Seiichi Manyama, Table of n, a(n) for n = 1..10000

Cf. A084432, A373184.

def A(k, n)
  ary = [0]
  (1..n).each{|i|
    j = i + 1
    j += ary[i / k] if i % k == 0
    ary << j
  }
  ary[1..-1]
end
p A(4, 90)

a(4*n+1) = 4*n+2, a(4*n+2) = 4*n+3, a(4*n+3) = 4*n+4 and a(4*n+4) = 4*n+5 + a(n+1) for n >= 0.

G.f.: A(x) = Sum_{k>=0} (1/(1 - x^(4^k))^2 - 1).

cp's OEIS Frontend

A373184 G.f. A(x) satisfies A(x) = 1/(1 - x)^2 - 1 + A(x^3).

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