cp's OEIS Frontend

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

%I A265360 #16 Jun 08 2021 09:22:32
%S A265360 6,8,12,13,19,25,29,43,53,67,94,131,173,214,269,359,479,713,863,1277,
%T A265360 1499,2099,3019,3833,5639,7103,10463,12527,18899,22643,33647,45989,
%U A265360 60443,88379,103319,166319,206639,280223,384479,543659,755663,1020599,1316699,1856159,2556839,3346559,4895963,6649199,8666783
%N A265360 Second smallest number of complexity n: second smallest number requiring n 1's to build using + and *.
%C A265360 As the first term of A005421 > 1 is A005421(5), the starting offset of this sequence is 5.
%C A265360 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 A265360 Jānis Iraids, <a href="/A265360/b265360.txt">Table of n, a(n) for n = 5..89</a>
%o A265360 (Python)
%o A265360 def aupton(nn):
%o A265360   alst, R = [], {0: {1}} # R[n] is set reachable using n+1 1's (n ops)
%o A265360   for n in range(1, nn):
%o A265360     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 A265360     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 A265360     new = R[n] - R[n-1]
%o A265360     if n >= 4: alst.append(min(new - {min(new)}))
%o A265360   return alst
%o A265360 print(aupton(35)) # _Michael S. Branicky_, Jun 08 2021
%Y A265360 Cf. A005245, A005421, A005520.
%K A265360 nonn
%O A265360 5,1
%A A265360 _Antti Karttunen_, with terms computed by _Janis Iraids_, Dec 15 2015