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A124934
Numbers of the form 4mn - m - n, where m, n are positive integers.
6
2, 5, 8, 11, 12, 14, 17, 19, 20, 23, 26, 29, 30, 32, 33, 35, 38, 40, 41, 44, 47, 50, 52, 53, 54, 56, 59, 61, 62, 63, 65, 68, 71, 74, 75, 77, 80, 82, 83, 85, 86, 89, 90, 92, 95, 96, 98, 101, 103, 104, 107, 109, 110, 113, 116, 117, 118, 119, 122, 124, 125, 128, 129, 131
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.
Complement of A094178; A125203(a(n)) > 0; union of A125217 and A125218; range of A125199. - Reinhard Zumkeller, Nov 24 2006
REFERENCES
L. E. Dickson, History of the Theory of Numbers, Vol. II, Diophantine Analysis. Dover Publications, Inc., Mineola, NY, 2005, p. 401.
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
Sequence in context: A327138 A102624 A070328 * A125217 A277574 A177966
KEYWORD
easy,nonn
AUTHOR
Nick Hobson, Nov 13 2006
EXTENSIONS
More terms from Reinhard Zumkeller, Nov 24 2006
STATUS
approved