OFFSET
1,1
COMMENTS
a(n) misses the squares since (2x)^2 + 1 = (4m - 1)(4n - 1) is impossible.
a(n) misses the triangular numbers since (2x + 1)^2 + 1 = 2(4m - 1)(4n - 1) is impossible.
Taking m = k(k - 1)/2, n = k(k + 1)/2 gives 4mn - m - n = (k^2 - 1)^2 - 1, so a(n) is one less than a square infinitely often.
REFERENCES
L. E. Dickson, History of the Theory of Numbers, Vol. II, Diophantine Analysis. Dover Publications, Inc., Mineola, NY, 2005, p. 401.
LINKS
N. Hobson, Table of n, a(n) for n = 1..1000
EXAMPLE
a(1) = 2 because 2 = 4*1*1 - 1 - 1 is the smallest value in the sequence.
PROG
(Haskell)
import Data.List (findIndices)
a124934 n = a124934_list !! (n-1)
a124934_list = map (+ 1) $ findIndices (> 0) a125203_list
-- Reinhard Zumkeller, Jan 02 2013
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Nick Hobson, Nov 13 2006
EXTENSIONS
More terms from Reinhard Zumkeller, Nov 24 2006
STATUS
approved