OFFSET
1,2
COMMENTS
Or, numerator of 1/1 + 1/3 + ... + 1/(2n-1) up to a(38).
Following similar remark by T. D. Noe in A025547, this coincides with f(n) = numerator of 1 + 1/3 + 1/5 + 1/7 + ... + 1/(2n-1) iff n <= 38. But a(39) = 18048708369314455836683437302413, f(39) = 1640791669937677803334857936583. Note that f(n) = numerator(digamma(n+1/2)/2 + log(2) + euler_gamma/2). - Paul Barry, Aug 19 2005 [See A350669(n-1).]
2*(1 + 1/3 + ... + 1/(2*n-1))/Pi = 2*a(n)/(A025547(n)*Pi) is the equivalent resistance between the points (0,0) and (n,n) on a 2-dimension infinite square grid of unit resistors. - Jianing Song, Apr 28 2025
LINKS
Georg Fischer, Table of n, a(n) for n = 1..200 (first 39 terms from Jean-François Alcover)
MathPages, The Algebra of an Infinite Grid of Resistors
Physics Stack Exchange, On this infinite grid of resistors, what's the equivalent resistance?
Eric Weisstein's World of Mathematics, Jeep Problem
FORMULA
1 + 1/3 + ... + 1/(2*n-1) = a(n)/A025547(n) = A350669(n-1)/A350670(n-1). - Jianing Song, Apr 28 2025
MAPLE
a:= n-> (f-> add(1/p, p=f)*ilcm(f[]))([2*i-1$i=1..n]):
seq(a(n), n=1..40); # Alois P. Heinz, Apr 16 2015
MATHEMATICA
Table[(Total[1/Range[1, 2n-1, 2]])LCM@@Range[1, 2n-1, 2], {n, 30}] (* Harvey P. Dale, Sep 09 2020 *)
PROG
(Haskell)
a025550 n = numerator $ sum $ map (1 %) $ take n [1, 3 ..]
-- Reinhard Zumkeller, Jan 22 2012
(PARI) a(n)=my(v=vector(n, i, 2*i-1)); sum(i=1, #v, 1/v[i])*lcm(v) \\ Charles R Greathouse IV, Feb 28 2013
(Magma) [&+[1/d: d in i]*Lcm(i) where i is [1..2*n-1 by 2]: n in [1..21]]; // Bruno Berselli, Apr 16 2015
CROSSREFS
KEYWORD
nonn,easy,nice
AUTHOR
EXTENSIONS
Value of a(39) corrected by Jean-François Alcover, Apr 16 2015
STATUS
approved