A212289 Record values in A002487.

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, 55, 60, 67, 69, 76, 79, 89, 97, 108, 109, 123, 128, 129, 131, 144, 157, 175, 178, 181, 199, 207, 208, 233, 254, 257, 283, 287, 322, 335, 337, 338, 343, 377, 411, 458, 465, 467, 474

Offset: 1

Author

Charles R Greathouse IV, Jun 13 2012

Keywords

• nonn

Comments

Distinct elements of A270362. - Jeffrey Shallit, Mar 16 2016.

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..646
• Ali Keramatipour and Jeffrey Shallit, Record-Setters in the Stern Sequence, arXiv:2205.06223 [math.CO], 2022.

Crossrefs

Cf. A002487, A212288.

Programs

Mathematica

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 *)

PARI

fusc(n)=my(a=1, b=0); while(n, if(n%2, b+=a, a+=b); n>>=1); b
r=-1;for(n=0,1e5,t=fusc(n); if(t>r,r=t;print1(t", ")))

Python

from itertools import count, islice
from functools import reduce
def A212289_gen(): # generator of terms
    yield (c:= 0)
    for n in count(1):
        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)))
        if m>c: yield (c:=m)
A212289_list = list(islice(A212289_gen(),30)) # Chai Wah Wu, Sep 23 2024

Formula

a(n) = fusc(A212288(n)).

Extensions

a(1)=0 prepended in terms, b-file and programs by Georg Fischer, Jun 24 2020