1,2

Numerators are A118835. A118835/A118836 converges to semiprime continued fraction constant ~ 4.147. Fractions are 4/1, 25/6, 229/55, 2326/559, 8231/1979, 1663/400, 1675/403, 37102/8929, 933094/224611, 6099761/1468634, 6127061/1475459, 209220974/50390831, 210096134/50609621, 2003570923/482705812, 2011032223/484571137, 92798472958/22363019977, 651501535306/157019195989, 653338770706/157478504839, 655042388986/157904409409, 594467821319054/143352242463851, 9545375103547/2301429052243, 593171891998214/143028260133641, 656686231186/158315369959, 595688624302454/143657443209701, 11041298401059049/2662927412245381. These are to semiprimes as A001053 are to natural numbers. See also A105815 Decimal expansion of the semiprime nested radical.

Eric Weisstein's World of Mathematics, Continued Fraction Constant.

a(n) = denominator of continued fraction [4; 6, 9, 10, 14, ... A001358(n)]. CONTINUANT transform of A001358.

a(1) = 1 = denominator of 4/1.

a(2) = 6 = denominator of 25/6 = 4+1/6.

a(3) = 55 = denominator of 229/55 = 4+1/(6+1/9).

a(4) = 559 = denominator of 2326/559 = 4+1/(6+1/9+(1/10)).

a(5) = 1979 = denominator of 8231/1979 = 4+1/(6+1/9+(1/10+(1/14))).

a(6) = 400 = denominator of 1663/400 = 4+1/(6+1/9+(1/10+(1/14+(1/15)))).

a(7) = 403 = denominator of 1675/403 = 4+1/(6+1/9+(1/10+(1/14+(1/15+(1/21))))).

a(8) = 8929 = denominator of 37102/8929 = 4+1/(6+1/9+(1/10+(1/14+(1/15+1/21+(1/22))))).

a(9) = 224611 = denominator of 933094/224611 = 4+1/(6+1/9+(1/10+(1/14+(1/15+(1/21+(1/22+ (1/25))))))).

a(20) = 158315369959 = denominator of 656686231186/158315369959 = 4+1/(6+1/9+(1/10+(1/14+(1/15+(1/21+(1/22+ (1/25+(1/26+(1/33+(1/34+(1/35+(1/38+(1/39+(1/46+(1/49+(1/51+(1/55+(1/57)))))))))))))))))).

Cf. A001358, A001040, A001053, A105815, A118835.

Sequence in context: A009577 A097300 A110431 this_sequence A079589 A006200 A095652

Adjacent sequences: A118833 A118834 A118835 this_sequence A118837 A118838 A118839

easy,frac,nonn

Jonathan Vos Post (jvospost3(AT)gmail.com), May 01 2006