A187922 Positions k of addition steps in Recamán's sequence where A005132(k-1)-k = A005132(m) for some 0 < m < k.

6, 7, 9, 18, 19, 21, 33, 34, 36, 66, 67, 69, 71, 73, 75, 101, 102, 104, 106, 108, 113, 114, 115, 117, 121, 123, 125, 127, 133, 134, 172, 173, 175, 177, 179, 181, 183, 186, 188, 189, 190, 194, 224, 225, 227, 229, 231, 233, 236, 238, 240, 242, 244, 246, 287, 288, 290, 292, 294, 296, 298, 300, 302, 304, 339, 340, 342, 344, 346, 348, 350

Offset: 1

Author

Reinhard Zumkeller, Mar 17 2011

Keywords

• nonn

Comments

Subsequence of A057165; A005132(a(n)-1) - a(n) = A005132(A187943(n));

A005132(a(n)) = A005132(a(n)-1) + a(n);

See A187921 for the other positions of addition steps in A005132.

Examples

			a(5) = 19: A005132(19-1) = 43 and 43-19>0, but the term 24=43-19 is already in A005132, therefore A005132(19)=43+19=62; A187943(5)=15 and A005132(15)=24.
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..25000
• Rémy Sigrist, C++ program for A187943
• Index entries for sequences related to Recamán's sequence

Crossrefs

Cf. A005132, A057165, A187921, A187943, A333548, A333552.

Programs

Haskell

import Data.Set (Set, singleton, member, insert)
a187922 n = a187922_list !! (n-1)
a187922_list = r (singleton 0) 1 0 where
   r :: Set Integer -> Integer -> Integer -> [Integer]
   r s n x | x <= n           = r (insert (x+n) s) (n+1) (x+n)
           | (x-n) `member` s = n : r (insert (x+n) s) (n+1) (x+n)
           | otherwise        = r (insert (x-n) s) (n+1) (x-n)
(C++) See Links section.

Extensions

Added condition "0 < m" to definition. See A333552. - N. J. A. Sloane, May 04 2020