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A354255 Even numbers in A090252 in order of appearance.

%I A354255 #47 Jul 15 2022 10:37:18
%S A354255 2,4,8,16,26,32,64,128,206,256,478,512,998,1024,2048,3134,4096,6514,
%T A354255 8192,13942,16384,28894,32768,60518,65536,126634,131072,261398,262144
%N A354255 Even numbers in A090252 in order of appearance.
%C A354255 The n-th even term in A090252 appears at index k <= A083329(n).
%C A354255 Conjecture: The indices of even numbers in A090252 are precisely the numbers {A083329(n), n >= 1}. See A090252 for discussion. - _N. J. A. Sloane_, May 22 2022
%C A354255 Taking logs to base 2 of these terms produces 1., 2., 3., 4., 4.700439718, 5., 6., 7., 7.686500527, 8., 8.900866807, 9., 9.962896004, 10., 11., 11.61378946, 12., 12.66932800, 13., 13.76714991, 14. - _N. J. A. Sloane_, Jun 01 2022
%o A354255 (Python)
%o A354255 from math import gcd, prod
%o A354255 from itertools import count, islice
%o A354255 def agen(): # generator of terms
%o A354255     alst, aset, mink = [1], {1}, 2
%o A354255     for n in count(2):
%o A354255         k, s = mink, n - n//2
%o A354255         prodall = prod(alst[n-n//2-1:n-1])
%o A354255         while k in aset or gcd(prodall, k) != 1: k += 1
%o A354255         alst.append(k); aset.add(k)
%o A354255         if k%2 == 0: yield k
%o A354255         while mink in aset: mink += 1
%o A354255 print(list(islice(agen(), 9))) # _Michael S. Branicky_, May 23 2022
%Y A354255 Cf. A083329, A090252, A247665, A248379, A353730, A354146, A354159.
%K A354255 nonn,more
%O A354255 1,1
%A A354255 _Michael S. Branicky_, May 21 2022
%E A354255 a(14) from _Michael S. Branicky_, May 26 2022
%E A354255 a(15)-a(21) from _Michael S. Branicky_, Jun 01 2022 using gzipped b-file in A090252
%E A354255 a(22)-a(26) from _Hugo van der Sanden_, Jun 14 2022
%E A354255 a(27)-a(29) from _Jinyuan Wang_, Jul 15 2022