A050049 a(n) = a(n-1) + a(m) for n >= 3, 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) = 2.
1, 2, 3, 5, 6, 11, 14, 16, 17, 33, 47, 58, 64, 69, 72, 74, 75, 149, 221, 290, 354, 412, 459, 492, 509, 525, 539, 550, 556, 561, 564, 566, 567, 1133, 1697, 2258, 2814, 3364, 3903, 4428, 4937, 5429, 5888, 6300, 6654, 6944, 7165, 7314
Offset: 1
Keywords
Examples
From _Petros Hadjicostas_, Nov 13 2019: (Start) We explain _Amarnath Murthy_'s process (see the Comments above). a(3) = a(2) + a(1) = 3. [Now a(3) is the last term available.] a(4) = a(3) + a(2) = 5. a(5) = a(3) + a(2) + a(1) = 6. [Now a(5) is the last term available.] a(6) = a(5) + a(4) = 11. a(7) = a(5) + a(4) + a(3) = 14. a(8) = a(5) + a(4) + a(3) + a(2) = 16. a(9) = a(5) + ... + a(1) = 17. [Now a(9) is the last term available.] a(10) = a(9) + a(8) = 33. a(11) = a(9) + a(8) + a(7) = 47. ... a(17) = a(9) + a(8) + ... + a(1) = 75. [Now a(17) is the last term available.] a(18) = a(17) + a(16) = 149. (End)
Links
- Ivan Neretin, Table of n, a(n) for n = 1..8193
Crossrefs
Programs
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Maple
a := proc(n) option remember; `if`(n < 3, [1, 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 13 2019
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Mathematica
Fold[Append[#1, #1[[-1]] + #1[[#2]]] &, {1, 2, 3}, Flatten@Table[k, {n, 5}, {k, 2^n, 1, -1}]] (* Ivan Neretin, Sep 07 2015 *)
Extensions
Name edited by Petros Hadjicostas, Nov 13 2019
Comments