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

Author

Eric Angelini, Aug 13 2006

Keywords

• nonn

Comments

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

Examples

			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.
		

Links

• 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

Crossrefs

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

Extensions

More terms from Max Alekseyev, Aug 14 2006

Edited by Max Alekseyev, Mar 08 2015