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

1,1

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.

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

Cf. A000290, A000217.

Sequence in context: A327138 A102624 A070328 * A125217 A277574 A177966

Adjacent sequences: A124931 A124932 A124933 * A124935 A124936 A124937

Keyword

easy,nonn

Author

Nick Hobson, Nov 13 2006

Extensions

More terms from Reinhard Zumkeller, Nov 24 2006

Status

approved