A121173 -id:A121173 - cp's OEIS frontend

A105753 Lexicographically earliest sequence of positive integers with the property that a(a(n)) = a(1)+a(2)+...+a(n).

1, 3, 4, 8, 6, 22, 9, 16, 53, 11, 133, 13, 279, 15, 573, 69, 18, 1233, 20, 2486, 23, 44, 4995, 25, 10059, 27, 20145, 29, 40319, 31, 80669, 33, 161371, 35, 322777, 37, 645591, 39, 1291221, 41, 2582483, 43, 5165009, 5039, 46, 10335103, 48

Offset: 1

Eric Angelini, Aug 13 2006

nonn

The Fibonacci 9-step numbers referenced in the Noe-Post paper are in A104144. - T. D. Noe, Oct 27 2008

			Sequence reads from the beginning:
- at position a(1)=1 we see the sum of all previously written terms [indeed, nil + 1=1]
- at position a(2)=3 we see the sum of all previously written terms [indeed, 1+ 3=4]
- at position a(3)=4 we see the sum of all previously written terms [indeed, 1+3+4=8]
- at position a(4)=8 we see the sum of all previously written terms [indeed, 1+3+4+8=16]
- at position a(5)=6 we see the sum of all previously written terms [indeed, 1+3+4+8+6=22]
- at position a(6)=22 we see the sum of all previously written terms [indeed, 1+3+4+8+6+22=44 and 44 is the 22nd term of S]
etc.

Alois P. Heinz, Table of n, a(n) for n = 1..1000
Tony D. Noe and Jonathan Vos Post, Primes in Fibonacci n-step and Lucas n-step Sequences, J. of Integer Sequences 8 (2005), Article 05.4.4

Cf. A121053, A121173, A121174, A121175, A104144.

More terms from Max Alekseyev, Aug 14 2006

Edited by Max Alekseyev, Mar 08 2015

A145654 Partial sums of A000918, starting from index 1.

Original entry on oeis.org

0, 2, 8, 22, 52, 114, 240, 494, 1004, 2026, 4072, 8166, 16356, 32738, 65504, 131038, 262108, 524250, 1048536, 2097110, 4194260, 8388562, 16777168, 33554382, 67108812, 134217674, 268435400, 536870854, 1073741764, 2147483586

Offset: 1

Vladimir Joseph Stephan Orlovsky, Oct 16 2008

			For n=7, a(7) = 6*2 + 5*2^2 + 4*2^3 + 3*2^4 + 2*2^5 + 1*2^6 = 240. - _Bruno Berselli_, Feb 10 2014
From _Bruno Berselli_, Jul 17 2018: (Start)
Row sums of the triangle:
   0   ......................................    0
   1,  1   ..................................    2
   3,  2,  3   ..............................    8
   6,  5,  5,  6   ..........................   22
  10, 11, 10, 11, 10   ......................   52
  15, 21, 21, 21, 21, 15   ..................  114
  21, 36, 42, 42, 42, 36, 21   ..............  240
  28, 57, 78, 84, 84, 78, 57, 28   ..........  494, etc.
(End)

Reinhard Zumkeller, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (4,-5,2).

Cf. A000217, A000295, A000918, A005803, A121173.

a145654 n = a145654_list !! (n-1)
a145654_list = scanl1 (+) $ tail a000918_list
-- Reinhard Zumkeller, Nov 06 2013

Accumulate[2^Range[30] - 2] (* or *) LinearRecurrence[{4, -5, 2}, {0, 2, 8}, 30] (* Harvey P. Dale, Jul 15 2017 *)

a(n) = Sum_{i=1..n} A000918(i).
a(n+1) - a(n) = A000918(n+1).
a(n) = A005803(n+1). - R. J. Mathar, Oct 21 2008
From Colin Barker, Jan 11 2012: (Start)
a(n) = 2*(-1 + 2^n - n).
G.f.: 2*x^2/((1-x)^2*(1-2*x)). (End)
a(n+1) = A121173(2*n). - Reinhard Zumkeller, Nov 06 2013
a(n) = Sum_{i=1..n-1} (n-i)*2^i with a(1)=0. - Bruno Berselli, Feb 10 2014
a(n) = 2 * A000295(n). - Alois P. Heinz, May 28 2018

Edited by R. J. Mathar, Oct 21 2008

A121175 Sequence S with the following properties: (i) a(1)=2; (ii) for n is S, a(n)=a(1)+a(2)+...+a(n-1); (iii) for n not in S, a(n)=the smallest number different from a(1), ..., a(n-1) not breaking property (ii).

Original entry on oeis.org

2, 2, 4, 8, 3, 7, 26, 52, 10, 114, 12, 240, 14, 494, 16, 1004, 18, 2026, 20, 4072, 22, 8166, 24, 16356, 27, 32739, 65478, 29, 130985, 31, 262001, 33, 524035, 35, 1048105, 37, 2096247, 39, 4192533, 41, 8385107, 43, 16770257, 45, 33540559

Offset: 1

Max Alekseyev, Aug 15 2006

nonn

Taking a(1)=2 makes all terms distinct except for a(1)=a(2)=2

Cf. A105753, A121053, A121174, A121173.

cp's OEIS Frontend

A105753 Lexicographically earliest sequence of positive integers with the property that a(a(n)) = a(1)+a(2)+...+a(n).

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A145654 Partial sums of A000918, starting from index 1.

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A121175 Sequence S with the following properties: (i) a(1)=2; (ii) for n is S, a(n)=a(1)+a(2)+...+a(n-1); (iii) for n not in S, a(n)=the smallest number different from a(1), ..., a(n-1) not breaking property (ii).

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