A265360 Second smallest number of complexity n: second smallest number requiring n 1's to build using + and *.

6, 8, 12, 13, 19, 25, 29, 43, 53, 67, 94, 131, 173, 214, 269, 359, 479, 713, 863, 1277, 1499, 2099, 3019, 3833, 5639, 7103, 10463, 12527, 18899, 22643, 33647, 45989, 60443, 88379, 103319, 166319, 206639, 280223, 384479, 543659, 755663, 1020599, 1316699, 1856159, 2556839, 3346559, 4895963, 6649199, 8666783

Offset: 5

Author

Antti Karttunen, with terms computed by Janis Iraids, Dec 15 2015

Keywords

• nonn

Comments

As the first term of A005421 > 1 is A005421(5), the starting offset of this sequence is 5.

Only composites seem to be 6, 8, 12, 25, 94, 214, 713 and in many ways the sequence seems to have similar properties with A005520, the smallest number of complexity n.

Links

• Jānis Iraids, Table of n, a(n) for n = 5..89

Crossrefs

Cf. A005245, A005421, A005520.

Programs

Python

def aupton(nn):
  alst, R = [], {0: {1}} # R[n] is set reachable using n+1 1's (n ops)
  for n in range(1, nn):
    R[n]  = set(a+b for i in range(n//2+1) for a in R[i] for b in R[n-1-i])
    R[n] |= set(a*b for i in range(n//2+1) for a in R[i] for b in R[n-1-i])
    new = R[n] - R[n-1]
    if n >= 4: alst.append(min(new - {min(new)}))
  return alst
print(aupton(35)) # Michael S. Branicky, Jun 08 2021