A193927 -id:A193927 - cp's OEIS frontend

A062039 a(0) = 1; a(n+1) = a(n) - n if a(n) > n, otherwise a(n+1) = a(n) + a(a(n)).

1, 1, 2, 4, 1, 2, 4, 5, 7, 12, 3, 7, 12, 24, 11, 18, 3, 7, 12, 24, 5, 7, 12, 24, 1, 2, 4, 5, 7, 12, 24, 25, 27, 32, 59, 25, 27, 32, 59, 21, 28, 35, 60, 18, 30, 54, 9, 21, 28, 35, 60, 10, 13, 37, 69, 15, 33, 65, 8, 15, 33, 65, 4, 5, 7, 12, 24, 25, 27, 32, 59, 74, 3, 7, 12, 24, 25, 27

Offset: 0

Reinhard Zumkeller, Jul 12 2001

a(A193854(n)) = 1, n>0;

A123643 and A123644 give record values and their positions: A123643(n)=a(A123644(n)). - Reinhard Zumkeller, Oct 04 2006

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

A123643 and A123644 give record values and their positions: A123643(n)=a(A123644(n)).

Cf. A193926 (first differences), A193927.

a062039 n = a062039_list !! n
a062039_list = 1 : f 1 0 where
   f x n | x > n     = (x-n) : f (x-n) (n+1)
         | otherwise =    x' : f x' (n+1) where x' = x + a062039 x
-- Reinhard Zumkeller, Aug 10 2011

a[0] = 1; a[n_] := a[n] = If[a[n-1] > n-1, a[n-1] - (n-1), a[n-1] + a[a[n-1]]]; Table[a[n], {n, 0, 77}] (* Jean-François Alcover, Mar 20 2011 *)

A193926 First differences of A062039.

Original entry on oeis.org

0, 1, 2, -3, 1, 2, 1, 2, 5, -9, 4, 5, 12, -13, 7, -15, 4, 5, 12, -19, 2, 5, 12, -23, 1, 2, 1, 2, 5, 12, 1, 2, 5, 27, -34, 2, 5, 27, -38, 7, 7, 25, -42, 12, 24, -45, 12, 7, 7, 25, -50, 3, 24, 32, -54, 18, 32, -57, 7, 18, 32, -61, 1, 2, 5, 12, 1, 2, 5, 27, 15

Offset: 0

Reinhard Zumkeller, Aug 10 2011

sign

a(n) = A062039(n+1) - A062039(n);

a(A193927(n)) = - A193927(n).

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

a193926 n = a193926_list !! n
a193926_list = zipWith (-) (tail a062039_list) a062039_list

A193928 Numbers m such that A062039(m) <= A062039(m+1).

Original entry on oeis.org

0, 1, 2, 4, 5, 6, 7, 8, 10, 11, 12, 14, 16, 17, 18, 20, 21, 22, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 35, 36, 37, 39, 40, 41, 43, 44, 46, 47, 48, 49, 51, 52, 53, 55, 56, 58, 59, 60, 62, 63, 64, 65, 66, 67, 68, 69, 70, 72, 73, 74, 75, 76, 77, 78, 79, 80, 82

Offset: 1

Reinhard Zumkeller, Aug 10 2011

nonn

Complement of A193927, A062039(a(n)) <= A062039(a(n)+1).

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

A193854 is a subsequence.

import Data.List (findIndices)
a193928 n = a193928_list !! (n-1)
a193928_list = findIndices (0 <=) a193926_list

cp's OEIS Frontend

A062039 a(0) = 1; a(n+1) = a(n) - n if a(n) > n, otherwise a(n+1) = a(n) + a(a(n)).

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A193926 First differences of A062039.

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A193928 Numbers m such that A062039(m) <= A062039(m+1).

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