A124934 Numbers of the form 4mn - m - n, where m, n are positive integers.

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

Author

Nick Hobson, Nov 13 2006

Keywords

• easy
• nonn

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

Examples

			a(1) = 2 because 2 = 4*1*1 - 1 - 1 is the smallest value in the sequence.
		

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

Crossrefs

Cf. A000290, A000217.

Programs

Haskell

import Data.List (findIndices)
a124934 n = a124934_list !! (n-1)
a124934_list = map (+ 1) $ findIndices (> 0) a125203_list
-- Reinhard Zumkeller, Jan 02 2013

Extensions

More terms from Reinhard Zumkeller, Nov 24 2006