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

Author

Jean-François Alcover and Paul Curtz, Jun 11 2016

Keywords

• nonn

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

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

Crossrefs

Cf. A000265, A006519, A007814, A082392.

Programs

Mathematica

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

PARI

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

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).