A127367 Inverse permutation to A127366.

0, 2, 1, 5, 3, 7, 4, 10, 6, 12, 8, 14, 9, 17, 11, 19, 13, 21, 15, 23, 16, 26, 18, 28, 20, 30, 22, 32, 24, 34, 25, 37, 27, 39, 29, 41, 31, 43, 33, 45, 35, 47, 36, 50, 38, 52, 40, 54, 42, 56, 44, 58, 46, 60, 48, 62, 49, 65, 51, 67, 53, 69, 55, 71, 57, 73, 59, 75, 61, 77, 63, 79, 64

Offset

0,2

Comments

Let m be the largest number such that n >= m(m+1). If n is even, a(n) = n - m; otherwise a(n) = n + m + 1.

a(A005408(n)) > 0; a(A005843(n)) <= 0. [Reinhard Zumkeller, Oct 12 2011]

Links

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

Index entries for sequences that are permutations of the natural numbers

Prog

(Haskell)
a127367 n | even n    = n - m + 1
          | otherwise = n + m
          where m = length $ takeWhile (<= n) a002378_list
-- Reinhard Zumkeller, Oct 12 2011
(Python)
from math import isqrt
def A127367(n): return n+((isqrt((n<<2)|1)-1>>1)+1 if n&1 else -(isqrt((n<<2)|1)-1>>1)) # Chai Wah Wu, Feb 13 2026

Crossrefs

Cf. A127366, A002378, A000194.

Cf. A002378 (oblong numbers).

Sequence in context: A094512 A393039 A182650 * A054084 A296069 A058683

Adjacent sequences: A127364 A127365 A127366 * A127368 A127369 A127370

Keyword

nonn

Author

Franklin T. Adams-Watters, Jan 11 2007

Status

approved