A209273 Decimal expansion of the continued fraction with elements given by A209272.

1, 6, 4, 4, 9, 4, 8, 6, 5, 0, 1, 1, 5, 9, 5, 7, 5, 6, 0, 9, 6, 0, 7, 7, 9, 4, 5, 0, 9, 7, 8, 5, 8, 0, 9, 1, 5, 8, 6, 3, 2, 9, 5, 3, 4, 9, 6, 4, 6, 6, 4, 3, 8, 7, 5, 9, 3, 7, 0, 2, 7, 6, 9, 2, 1, 4, 9, 2, 3, 3, 6, 0, 1, 6, 3, 1, 8, 4, 4, 2, 4, 8, 4, 6, 0, 7, 0, 6, 8, 1, 1, 7, 9, 0, 0, 2, 8, 6, 7, 0, 8

Offset

1,2

Comments

The numerator and the denominator of the n-th convergent for this number are always squarefree. Close to zeta(2) = 1.644934066848...

Links

Table of n, a(n) for n=1..101.

Prog

(PARI) /*   realprecision = 202 significant digits */ v=[1]; for(k=1, 200, m=1; while(issquarefree(contfracpnqn(concat(v, [m]))[1, 1])+issquarefree(contfracpnqn(concat(v, [m]))[2, 1])<2, m++); v=concat(v, [m]); print((contfracpnqn(v)[1, 1])*1./(contfracpnqn(v)[2, 1]), ""))

Crossrefs

Cf. A209272.

Sequence in context: A110756 A200698 A013661 * A330934 A019174 A019166

Adjacent sequences: A209270 A209271 A209272 * A209274 A209275 A209276

Keyword

nonn,cons

Author

Benoit Cloitre, Jan 15 2013

Status

approved