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A212289 Record values in A002487.

%I A212289 #30 Sep 24 2024 06:06:34
%S A212289 0,1,2,3,4,5,7,8,9,11,13,14,15,18,19,21,23,26,29,30,34,37,41,47,49,50,
%T A212289 55,60,67,69,76,79,89,97,108,109,123,128,129,131,144,157,175,178,181,
%U A212289 199,207,208,233,254,257,283,287,322,335,337,338,343,377,411,458,465,467,474
%N A212289 Record values in A002487.
%C A212289 Distinct elements of A270362. - _Jeffrey Shallit_, Mar 16 2016.
%H A212289 Charles R Greathouse IV, <a href="/A212289/b212289.txt">Table of n, a(n) for n = 1..646</a>
%H A212289 Ali Keramatipour and Jeffrey Shallit, <a href="https://arxiv.org/abs/2205.06223">Record-Setters in the Stern Sequence</a>, arXiv:2205.06223 [math.CO], 2022.
%F A212289 a(n) = fusc(A212288(n)).
%t A212289 Union@ FoldList[Max, Nest[Append[#1, If[OddQ[#2], #1[[(#2 + 1)/2]], #1[[#2/2]] + #1[[(#2 + 2)/2]] ]] & @@ {#, Length@ # + 1} &, {0, 1}, 10^4]] (* _Michael De Vlieger_, Jul 10 2019 *)
%o A212289 (PARI) fusc(n)=my(a=1, b=0); while(n, if(n%2, b+=a, a+=b); n>>=1); b
%o A212289 r=-1;for(n=0,1e5,t=fusc(n); if(t>r,r=t;print1(t", ")))
%o A212289 (Python)
%o A212289 from itertools import count, islice
%o A212289 from functools import reduce
%o A212289 def A212289_gen(): # generator of terms
%o A212289     yield (c:= 0)
%o A212289     for n in count(1):
%o A212289         m = sum(reduce(lambda x,y:(x[0],x[0]+x[1]) if int(y) else (x[0]+x[1],x[1]),bin(n)[-1:2:-1],(1,0)))
%o A212289         if m>c: yield (c:=m)
%o A212289 A212289_list = list(islice(A212289_gen(),30)) # _Chai Wah Wu_, Sep 23 2024
%Y A212289 Cf. A002487, A212288.
%K A212289 nonn
%O A212289 1,3
%A A212289 _Charles R Greathouse IV_, Jun 13 2012
%E A212289 a(1)=0 prepended in terms, b-file and programs by _Georg Fischer_, Jun 24 2020