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

5,1

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

Prog

(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

Crossrefs

Cf. A005245, A005421, A005520.

Sequence in context: A222175 A350767 A315856 * A182253 A354098 A026601

Adjacent sequences: A265357 A265358 A265359 * A265361 A265362 A265363

Keyword

nonn

Author

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

Status

approved