A378030 Lexicographically earliest sequence of distinct positive integers such that a(a(n)) = a(a(n)-1) + a(a(n)-2).

3, 4, 7, 11, 6, 17, 23, 9, 32, 12, 44, 56, 14, 70, 16, 86, 102, 19, 121, 21, 142, 24, 166, 190, 26, 216, 28, 244, 30, 274, 33, 307, 340, 35, 375, 37, 412, 39, 451, 41, 492, 43, 535, 578, 46, 624, 48, 672, 50, 722, 52, 774, 54, 828, 57, 885, 942, 59, 1001, 61, 1062, 63, 1125, 65, 1190, 67, 1257, 69, 1326, 1395, 72, 1467, 74, 1541, 76, 1617, 78, 1695, 80

Offset: 1

Author

Scott R. Shannon, Nov 14 2024

Keywords

• nonn

Comments

A self-referencing Fibonacci sequence. The terms appear to be concentrated along two lines, a lower straight line where a(n) is approximately n and an upper curved line where a(n) ~ n^2/4.

The missing numbers are 1, 2, 5, 8, 10, 13, 15, 18, 20, 22, 25, 27, 29, 31, ... .

Examples

			a(1) = 3 as a(3) = 7 and a(3-1) + a(3-2) = 4 + 3 = 7.
		

Links

• Scott R. Shannon, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000045, A105753, A007378, A004001, A005185, A121053.