A095901 -id:A095901 - cp's OEIS frontend

A283480 Partial sums of A095901.

1, 2, 2, 2, 3, 3, 3, 3, 4, 4, 5, 6, 6, 6, 6, 6, 7, 7, 8, 8, 8, 9, 9, 9, 10, 11, 12, 12, 12, 12, 12, 12, 13, 13, 14, 14, 15, 16, 16, 17, 17, 17, 18, 18, 18, 19, 20, 21, 21, 22, 23, 23, 23, 23, 24, 25, 26, 27, 27, 27, 27, 27, 27, 27, 28, 28, 29, 29, 30, 30, 30, 31, 31, 32, 32, 32, 33, 33, 34, 35, 35, 36, 37, 37, 37, 37, 38, 38, 39, 40, 40, 41

Offset: 1

Antti Karttunen, Mar 18 2017

nonn

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

The least monotonic left inverse of A283481.

Cf. A004001, A095901, A095902.

a[n_] := a[n] = If[n <= 2, 1, a[a[n - 1]] + a[n - a[n - 1]]]; Accumulate@ Table[Mod[a@ n, 2], {n, 92}] (* Michael De Vlieger, Mar 18 2017, after Robert G. Wilson v at A004001 *)

a(1) = 1; for n > 1, a(n) = A095901(n) + a(n-1).
Other identities. For all n >= 1:
a(A283481(n)) = n.
a(2^n) = A095902(n).

A140591 Duplicate of A095901.

Original entry on oeis.org

0, 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

Offset: 0

Roger L. Bagula and Gary W. Adamson, Jul 06 2008

dead

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

A283482 Positions of even terms in A004001.

Original entry on oeis.org

3, 4, 6, 7, 8, 10, 13, 14, 15, 16, 18, 20, 21, 23, 24, 28, 29, 30, 31, 32, 34, 36, 39, 41, 42, 44, 45, 49, 52, 53, 54, 59, 60, 61, 62, 63, 64, 66, 68, 70, 71, 73, 75, 76, 78, 81, 84, 85, 86, 88, 91, 94, 95, 96, 98, 99, 103, 104, 105, 106, 108, 109, 113, 114, 115, 116, 122, 123, 124, 125, 126, 127, 128, 130, 132, 134, 137, 139, 141, 142, 144

Offset: 1

Antti Karttunen, Mar 18 2017

nonn

Antti Karttunen, Table of n, a(n) for n = 1..8264

Cf. A283481 (complement), A283471 (a subsequence).
Positions of zeros in A095901.
Cf. A004001.

a[n_] := a[n] = If[n <= 2, 1, a[a[n - 1]] + a[n - a[n - 1]]]; Select[Range@ 144, EvenQ@ a[#] &] (* Michael De Vlieger, Mar 18 2017, after Robert G. Wilson v at A004001 *)

cp's OEIS Frontend

A283480 Partial sums of A095901.

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A140591 Duplicate of A095901.

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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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A283482 Positions of even terms in A004001.

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