A295087 - OEIS

%I #26 May 19 2023 07:01:49

%S 0,1,2,3,4,5,7,8,6,9,11,10,13,12,14,15,18,17,19,21,16,23,22,26,29,25,

%T 24,27,30,34,31,20,28,33,37,32,35,41,40,47,43,44,36,39,49,46,50,55,45,

%U 38,52,51,60,53,57,48,42,56,67,63,69,76,65,61,68,58,71,64

%N Distinct values in A002487 in the order of appearance.

%C This sequence is a permutation of the nonnegative integers, with inverse A295088.

%H Rémy Sigrist, <a href="/A295087/b295087.txt">Table of n, a(n) for n = 1..10000</a>

%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>

%H <a href="/index/St#Stern">Index entries for sequences related to Stern's sequences</a>

%F a(n) = A002487(A091945(n)).

%e The first terms of this sequence, alongside the first terms of A002487, are:

%e n   a(n)    fusc(k) k

%e --  ----    ------- --

%e 1   0       0       0

%e 2   1       1       1

%e .   .       1       2

%e 3   2       2       3

%e .   .       1       4

%e 4   3       3       5

%e .   .       2       6

%e .   .       3       7

%e .   .       1       8

%e 5   4       4       9

%e .   .       3       10

%e 6   5       5       11

%e .   .       2       12

%e .   .       5       13

%e .   .       3       14

%e .   .       4       15

%e .   .       1       16

%e .   .       5       17

%e .   .       4       18

%e 7   7       7       19

%e .   .       3       20

%e 8   8       8       21

%e .   .       5       22

%e .   .       7       23

%o (PARI) fusc(n)=local(a=1, b=0); while(n>0, if(bitand(n, 1), b+=a, a+=b); n>>=1); b \\ after _Charles R Greathouse IV_ at A002487

%o s=0; for (n=0, 621, v=fusc(n); if(!bittest(s,v), print1(v", "); s+=2^v))

%o (Python)

%o from functools import reduce

%o from itertools import count, islice

%o def A295087_gen(): # generator of terms

%o     s = {0}

%o     yield 0

%o     for n in count(1):

%o         if (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)))) not in s:

%o             yield m

%o             s.add(m)

%o A295087_list = list(islice(A295087_gen(),20)) # _Chai Wah Wu_, May 18 2023

%Y Cf. A002487, A091945, A295088.

%K nonn

%O 1,3

%A _Rémy Sigrist_, Nov 14 2017

%E Formula adapted after change in A091945 by _Rémy Sigrist_, Dec 07 2022