1,2

Found by exhaustive search. Program produces all values that are combinations of two binary operators a() and b() (here "sum" and "reciprocal sum of reciprocals") over n occurrences of 1. E.g. given 4 occurrences of 1, the code forms all allowable postfix forms, such as 1 1 1 1 a a a and 1 1 b 1 1 a b, etc. Each resulting form is then evaluated according to the definitions for a and b.

Each resistance that can be constructed from n 1-ohm resistors in a circuit can be written as the ratio of two positive integers, neither of which exceeds the (n+1)st Fibonacci number. E.g., for n=4, the 9 resistances that can be constructed can be written as 1/4, 2/5, 3/5, 3/4, 1/1, 4/3, 5/3, 5/2, 4/1 using no numerator or denominator larger than Fib(n+1) = Fib(5) = 5. If a resistance x can be constructed from n 1-ohm resistors, then a resistance 1/x can also be constructed from n 1-ohm resistors. - Jon E. Schoenfield (jonscho(AT)hiwaay.net), Aug 06 2006

a(2) = 2 since given two 1-ohm resistors, a series circuit yields 2 ohms, while a parallel circuit yields 1/2 ohms.

Let T(x, n) = 1 if x can be constructed with n 1-ohm resistors in a circuit, 0 otherwise. Then A048211 is t(n) = sum(T(x, n)) for all x (x is necessarily rational). Let H(x, n) = 1 if T(x, n) = 1 and T(x, k) = 0 for all k < n, 0 otherwise. Then A051389 is h(n) = sum(H(x, n)) for all x (x is necessarily rational).

Sequence in context: A129875 A055094 A055729 this_sequence A098719 A115324 A107092

Adjacent sequences: A048208 A048209 A048210 this_sequence A048212 A048213 A048214

nonn,nice,more

Tony Bartoletti (azb(AT)llnl.gov)

More terms from John W. Layman (layman(AT)math.vt.edu), Apr 06 2002

a(16) through a(21) from Jon E. Schoenfield (jonscho(AT)hiwaay.net), Aug 06 2006

a(22) from Jon E. Schoenfield (jonscho(AT)hiwaay.net), Aug 28 2006