A265404 a(n) = number of Spironacci numbers (A078510) needed to sum to n using the greedy algorithm.

0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 2, 1, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2

Offset: 0

Author

Antti Karttunen, Dec 16 2015

Keywords

• nonn

Comments

a(0) = 0, because no numbers are needed to form an empty sum, which is zero.

First 2 occurs as a(17), first 3 at a(234), first 4 at a(3266).

Examples

			For n=17, the largest Spironacci number <= 17 is 16 (= A078510(22)). 17 - 16 = 1, which is A078510(1), thus 17 = A078510(22) + A078510(1), requiring only two such numbers for its sum, thus a(17) = 2.
For n=234, the largest Spironacci number <= 234 is 217 (= A078510(45)). 234-217 = 17 (whose decomposition is shown above), so 234 = A078510(45) + A078510(22) + A078510(1), thus a(234) = 3.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 0..10132

Crossrefs

Cf. A078510 (from its term a(7) onward gives also the positions of ones here).

Cf. also A007895, A053610, A265743, A265744, A265745.