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Second smallest number of complexity n: second smallest number requiring n 1's to build using + and *.
3

%I #16 Jun 08 2021 09:22:32

%S 6,8,12,13,19,25,29,43,53,67,94,131,173,214,269,359,479,713,863,1277,

%T 1499,2099,3019,3833,5639,7103,10463,12527,18899,22643,33647,45989,

%U 60443,88379,103319,166319,206639,280223,384479,543659,755663,1020599,1316699,1856159,2556839,3346559,4895963,6649199,8666783

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

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

%C 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.

%H Jānis Iraids, <a href="/A265360/b265360.txt">Table of n, a(n) for n = 5..89</a>

%o (Python)

%o def aupton(nn):

%o alst, R = [], {0: {1}} # R[n] is set reachable using n+1 1's (n ops)

%o for n in range(1, nn):

%o R[n] = set(a+b for i in range(n//2+1) for a in R[i] for b in R[n-1-i])

%o R[n] |= set(a*b for i in range(n//2+1) for a in R[i] for b in R[n-1-i])

%o new = R[n] - R[n-1]

%o if n >= 4: alst.append(min(new - {min(new)}))

%o return alst

%o print(aupton(35)) # _Michael S. Branicky_, Jun 08 2021

%Y Cf. A005245, A005421, A005520.

%K nonn

%O 5,1

%A _Antti Karttunen_, with terms computed by _Janis Iraids_, Dec 15 2015