A274139 a(n) = 2^A000265(n) = 2^numerator(n/2^n), a sequence related to Oresme numbers.

2, 2, 8, 2, 32, 8, 128, 2, 512, 32, 2048, 8, 8192, 128, 32768, 2, 131072, 512, 524288, 32, 2097152, 2048, 8388608, 8, 33554432, 8192, 134217728, 128, 536870912, 32768, 2147483648, 2, 8589934592, 131072, 34359738368, 512, 137438953472, 524288, 549755813888, 32

Offset

1,1

Comments

Differences: 0, 6, -6, 30, -24, 120, -126, 510, -480, 2016, -2040, 8184, -8064, 32640, -32766, 131070, -130560, ...

GCD of differences is 6.

Links

Table of n, a(n) for n=1..40.

A. F. Horadam, Oresme numbers, Fib. Quart., 12 (1974), 267-271.

Formula

a(n) = 2^denominator(2^n/n).

a(n) = 2^(n/2^valuation(n,2)) = 2^A007814(n).

a(n) = 2*A082392(n)^2 (conjecture).

Mathematica

a[n_] := 2^(n/2^IntegerExponent[n, 2]);
Array[a, 40]

Prog

(PARI) a(n) = 2^(n/2^valuation(n, 2)); \\ Michel Marcus, Jun 12 2016

Crossrefs

Cf. A000265, A006519, A007814, A082392.

Sequence in context: A245497 A086328 A095997 * A283995 A056189 A331639

Adjacent sequences: A274136 A274137 A274138 * A274140 A274141 A274142

Keyword

nonn

Author

Jean-François Alcover and Paul Curtz, Jun 11 2016

Status

approved