A283480 -id:A283480 - cp's OEIS frontend

A095901 A004001 (mod 2).

1, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 1, 0, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1, 0, 0, 0, 1, 0, 1, 1, 0, 1, 1, 0, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0

Offset: 1

Robert G. Wilson v, Jun 12 2004

Antti Karttunen, Table of n, a(n) for n = 1..8192

Cf. A000035, A004001.
Cf. A095902 (number of odd entries less than or equal to 2^n).
Cf. A283480 (partial sums).
Characteristic function of A283481.

a[1] = a[2] = 1; a[n_] := a[n] = a[a[n - 1]] + a[n - a[n - 1]]; Table[ a[n], {n, 105}]

(define (A095901 n) (A000035 (A004001 n))) ;; Further code found under those two entries, Antti Karttunen, Mar 21 2017

a(n) = A004001(n) mod 2.

A283481 Positions of odd terms in A004001.

Original entry on oeis.org

1, 2, 5, 9, 11, 12, 17, 19, 22, 25, 26, 27, 33, 35, 37, 38, 40, 43, 46, 47, 48, 50, 51, 55, 56, 57, 58, 65, 67, 69, 72, 74, 77, 79, 80, 82, 83, 87, 89, 90, 92, 93, 97, 100, 101, 102, 107, 110, 111, 112, 117, 118, 119, 120, 121, 129, 131, 133, 135, 136, 138, 140, 143, 145, 148, 150, 151, 153, 154, 158, 160, 163, 165, 166, 168, 169

Offset: 1

Antti Karttunen, Mar 18 2017

nonn

Antti Karttunen, Table of n, a(n) for n = 1..8121

Cf. A283482 (complement), A283480 (a left inverse).
Positions of ones in A095901.
Cf. A004001.

a[n_] := a[n] = If[n <= 2, 1, a[a[n - 1]] + a[n - a[n - 1]]]; Select[Range@ 169, OddQ@ a[#] &] (* Michael De Vlieger, Mar 18 2017, after Robert G. Wilson v at A004001 *)

Other identities. For all n >= 1:

A283480(a(n)) = n.

A095902 Number of odd entries in A004001 that are <= 2^n.

Original entry on oeis.org

1, 2, 2, 3, 6, 12, 27, 55, 115, 235, 490, 994, 2008, 4036, 8120, 16280, 32640, 65344, 130879, 261935, 524057, 1048301, 2096855, 4193951, 8388239, 16776799, 33554339, 67109539, 134220995

Offset: 0

Robert G. Wilson v, Jun 12 2004

Even entries and odd entries are equal only when n=4, 6 and 12. Past that, the evens outnumber the odds.

Cf. A000079, A004001, A095901, A283480.

a[1] = a[2] = 1; a[n_] := a[n] = a[a[n - 1]] + a[n - a[n - 1]]; c = 0; k = 1; Do[ While[k <= 2^n, If[ Mod[ a[k], 2] == 1, c++ ]; k++ ]; Print[c], {n, 21}]

(define (A095902 n) (A283480 (A000079 n))) ;; Antti Karttunen, Mar 21 2017

a(n) = A283480(2^n) - Antti Karttunen, Mar 21 2017

a(22)-a(28) from Donovan Johnson, Jan 28 2009

cp's OEIS Frontend

A095901 A004001 (mod 2).

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A283481 Positions of odd terms in A004001.

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A095902 Number of odd entries in A004001 that are <= 2^n.

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