A050029 -id:A050029 - cp's OEIS frontend

A050061 a(n) = a(n-1) + a(m) for n >= 4, where m = 2^(p+1) + 2 - n and p is the unique integer such that 2^p < n - 1 <= 2^(p+1), starting with a(1) = 1, a(2) = 3, and a(3) = 2.

1, 3, 2, 5, 6, 11, 13, 16, 17, 33, 46, 57, 63, 68, 70, 73, 74, 147, 217, 285, 348, 405, 451, 484, 501, 517, 530, 541, 547, 552, 554, 557, 558, 1115, 1669, 2221, 2768, 3309, 3839, 4356, 4857, 5341, 5792, 6197, 6545, 6830, 7047, 7194

Offset: 1

Clark Kimberling

nonn

Ivan Neretin, Table of n, a(n) for n = 1..8193

Cf. similar sequences with different initial conditions: A050025 (1,1,1), A050029 (1,1,2), A050033 (1,1,3), A050037 (1,1,4), A050041 (1,2,1), A050045 (1,2,2), A050049 (1,2,3), A050053 (1,2,4), A050057 (1,3,1), A050065 (1,3,3), A050069 (1,3,4).

a := proc(n) option remember;
`if`(n < 4, [1, 3, 2][n], a(n - 1) + a(2^ceil(log[2](n - 1)) + 2 - n)); end proc;
seq(a(n), n = 1..50); # Petros Hadjicostas, Nov 11 2019

Fold[Append[#1, #1[[-1]] + #1[[#2]]] &, {1, 3, 2}, Flatten@Table[k, {n, 5}, {k, 2^n, 1, -1}]] (* Ivan Neretin, Sep 08 2015 *)

Name edited by Petros Hadjicostas, Nov 11 2019

A050065 a(n) = a(n-1) + a(m) for n >= 4, where m = 2^(p+1) + 2 - n and p is the unique integer such that 2^p < n - 1 <= 2^(p+1), starting with a(1) = 1 and a(2) = a(3) = 3.

Original entry on oeis.org

1, 3, 3, 6, 7, 13, 16, 19, 20, 39, 55, 68, 75, 81, 84, 87, 88, 175, 259, 340, 415, 483, 538, 577, 597, 616, 632, 645, 652, 658, 661, 664, 665, 1329, 1990, 2648, 3300, 3945, 4577, 5193, 5790, 6367, 6905, 7388, 7803, 8143, 8402, 8577

Offset: 1

Clark Kimberling

nonn

Ivan Neretin, Table of n, a(n) for n = 1..8193

Cf. similar sequences with different initial conditions: A050025 (1,1,1), A050029 (1,1,2), A050033 (1,1,3), A050037 (1,1,4), A050041 (1,2,1), A050045 (1,2,2), A050049 (1,2,3), A050053 (1,2,4), A050057 (1,3,1), A050061 (1,3,2), A050069 (1,3,4).

a := proc(n) option remember;
`if`(n < 4, [1, 3, 3][n], a(n - 1) + a(Bits:-Iff(n - 2, n - 2) + 3 - n)); end proc;
seq(a(n), n = 1 .. 48); # Petros Hadjicostas, Nov 08 2019

Fold[Append[#1, #1[[-1]] + #1[[#2]]] &, {1, 3, 3}, Flatten@Table[k, {n, 5}, {k, 2^n, 1, -1}]] (* Ivan Neretin, Sep 08 2015 *)

Name edited by Petros Hadjicostas, Nov 08 2019

A096116 a(1)=1, if n=(2^k)+1, a(n) = k+2, otherwise a(n) = 2+A000523(n-1)+a(2+A035327(n-1)).

Original entry on oeis.org

1, 2, 3, 5, 4, 9, 7, 6, 5, 11, 12, 14, 9, 10, 8, 7, 6, 13, 14, 16, 15, 20, 18, 17, 11, 12, 13, 15, 10, 11, 9, 8, 7, 15, 16, 18, 17, 22, 20, 19, 18, 24, 25, 27, 22, 23, 21, 20, 13, 14, 15, 17, 16, 21, 19, 18, 12, 13, 14, 16, 11, 12, 10, 9, 8, 17, 18, 20, 19, 24, 22, 21, 20, 26

Offset: 1

Amarnath Murthy, Jun 30 2004

nonn

Each n > 1 occurs A025147(n) times in the sequence.

Ivan Neretin, Table of n, a(n) for n = 1..10000

Cf. A096111, A050029, A050030, A052330, A096113, A096114, A096115.

a = {1}; Do[AppendTo[a, If[BitAnd[n - 1, n - 2] == 0, Log2[n - 1] + 2, 2 + Floor[Log2[n - 1]] + a[[2 + BitXor[n - 1, 2^Ceiling[Log2[n]] - 1]]]]], {n, 2, 74}]; a (* Ivan Neretin, Jun 24 2016 *)

(define (A096116 n) (cond ((= 1 n) 1) ((pow2? (- n 1)) (+ 2 (A000523 (- n 1)))) (else (+ 2 (A000523 (- n 1)) (A096116 (+ 2 (A035327 (- n 1))))))))
(define (pow2? n) (and (> n 0) (zero? (A004198bi n (- n 1)))))
;; Antti Karttunen, Aug 25 2006

Edited and extended by Antti Karttunen, Aug 25 2006

cp's OEIS Frontend

A050061 a(n) = a(n-1) + a(m) for n >= 4, where m = 2^(p+1) + 2 - n and p is the unique integer such that 2^p < n - 1 <= 2^(p+1), starting with a(1) = 1, a(2) = 3, and a(3) = 2.

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A050065 a(n) = a(n-1) + a(m) for n >= 4, where m = 2^(p+1) + 2 - n and p is the unique integer such that 2^p < n - 1 <= 2^(p+1), starting with a(1) = 1 and a(2) = a(3) = 3.

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Maple

Mathematica

Extensions

A096116 a(1)=1, if n=(2^k)+1, a(n) = k+2, otherwise a(n) = 2+A000523(n-1)+a(2+A035327(n-1)).

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