A371639 -id:A371639 - cp's OEIS frontend

A371638 a(n) = 2*n + valuation(n, 3) with valuation(n, 3) = A007949(n).

2, 4, 7, 8, 10, 13, 14, 16, 20, 20, 22, 25, 26, 28, 31, 32, 34, 38, 38, 40, 43, 44, 46, 49, 50, 52, 57, 56, 58, 61, 62, 64, 67, 68, 70, 74, 74, 76, 79, 80, 82, 85, 86, 88, 92, 92, 94, 97, 98, 100, 103, 104, 106, 111, 110, 112, 115, 116, 118, 121, 122, 124, 128, 128

Offset: 1

Peter Luschny, Mar 30 2024

See A371639 for the connection with Voronoi's congruence.

Cf. A007949, A371639, A292608 (c=2).

A371638 := n -> 2*n + padic:-ordp(n, 3): seq(A371638(n), n = 1..64);

Array[2 # + IntegerExponent[#, 3] &, 64] (* Michael De Vlieger, Mar 31 2024 *)

def A371638(n): return 2 * n + valuation(n, 3)
print([A371638(n) for n in range(1, 65)])

a(n) = valuation(denominator(Voronoi(3, n))) where Voronoi(c, n) = ((c^n - 1) * bernoulli(n)) / (n * c^(n - 1)).

A371640 a(n) = 3^(2*n + valuation(n, 3)) = 3^A371638(n).

Original entry on oeis.org

9, 81, 2187, 6561, 59049, 1594323, 4782969, 43046721, 3486784401, 3486784401, 31381059609, 847288609443, 2541865828329, 22876792454961, 617673396283947, 1853020188851841, 16677181699666569, 1350851717672992089, 1350851717672992089, 12157665459056928801, 328256967394537077627

Offset: 1

Peter Luschny, Mar 30 2024

nonn

See A371639 for the connection with Voronoi's congruence.

Cf. A371638, A371639 (numerator Voronoi).

A371640 := n -> 3^(2*n + padic:-ordp(n, 3)):
seq(A371640(n), n = 1..21);

def A371640(n): return 3**(2*n + valuation(n, 3))
print([A371640(n) for n in range(1, 22)])

a(n) = denominator(Voronoi(3, 2*n)) where Voronoi(c, n) = ((c^n - 1)*Bernoulli(n)) / (n*c^(n - 1)).

cp's OEIS Frontend

A371638 a(n) = 2*n + valuation(n, 3) with valuation(n, 3) = A007949(n).

Views

Author

Keywords

Comments

Crossrefs

Programs

Maple

Mathematica

SageMath

Formula