A360269 Least sum of 2's and 3's required to build n using +, * and parentheses.

2, 3, 4, 5, 5, 7, 6, 6, 7, 8, 7, 10, 9, 8, 8, 10, 8, 11, 9, 10, 10, 12, 9, 10, 11, 9, 11, 11, 10, 13, 10, 11, 12, 12, 10, 14, 12, 13, 11, 15, 12, 14, 12, 11, 14, 13, 11, 14, 12, 13, 13, 15, 11, 13, 13, 14, 13, 16, 12, 16, 14, 13, 12, 15, 13, 15, 14, 15, 14

Offset: 2

Author

Tamas Sandor Nagy, Jan 31 2023

Keywords

• nonn

Examples

			a(7) = 7 because 7 built by the rules is 2*2+3 or 2+2+3, and in both cases the sum is 7 and there is no other combination with a lesser sum.
a(17) = 10 because 17 = (2+3)*3+2, with 10 being the minimal sum.
a(22) = 10 because 22 = 2*(3*3+2) and these 2's and 3's add up to 10, which is the least possible sum.
a(44) = 12 because 44 = 2*2*(3*3+2), with the least possible sum being 12.
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 2..10000
• Index to sequences related to the complexity of n

Crossrefs

Cf. A000040, A025280.

Programs

PARI

seq(n)=my(a=vector(n)); for(n=1, #a, my(m=if(n==2||n==3, n, oo)); for(k=2, n-2, m=min(m, a[k]+a[n-k])); fordiv(n, d, if(d>1&&dAndrew Howroyd, Jan 31 2023

Extensions

Terms a(46) and beyond from Andrew Howroyd, Feb 01 2023