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A265360
Second smallest number of complexity n: second smallest number requiring n 1's to build using + and *.
3
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
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
KEYWORD
nonn
AUTHOR
Antti Karttunen, with terms computed by Janis Iraids, Dec 15 2015
STATUS
approved