A295087 Distinct values in A002487 in the order of appearance.

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, 24, 27, 30, 34, 31, 20, 28, 33, 37, 32, 35, 41, 40, 47, 43, 44, 36, 39, 49, 46, 50, 55, 45, 38, 52, 51, 60, 53, 57, 48, 42, 56, 67, 63, 69, 76, 65, 61, 68, 58, 71, 64

Offset

1,3

Comments

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

Links

Rémy Sigrist, Table of n, a(n) for n = 1..10000

Index entries for sequences that are permutations of the natural numbers

Index entries for sequences related to Stern's sequences

Formula

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

Example

The first terms of this sequence, alongside the first terms of A002487, are:
n   a(n)    fusc(k) k
--  ----    ------- --
1   0       0       0
2   1       1       1
.   .       1       2
3   2       2       3
.   .       1       4
4   3       3       5
.   .       2       6
.   .       3       7
.   .       1       8
5   4       4       9
.   .       3       10
6   5       5       11
.   .       2       12
.   .       5       13
.   .       3       14
.   .       4       15
.   .       1       16
.   .       5       17
.   .       4       18
7   7       7       19
.   .       3       20
8   8       8       21
.   .       5       22
.   .       7       23

Prog

(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
s=0; for (n=0, 621, v=fusc(n); if(!bittest(s, v), print1(v", "); s+=2^v))
(Python)
from functools import reduce
from itertools import count, islice
def A295087_gen(): # generator of terms
    s = {0}
    yield 0
    for n in count(1):
        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:
            yield m
            s.add(m)
A295087_list = list(islice(A295087_gen(), 20)) # Chai Wah Wu, May 18 2023

Crossrefs

Cf. A002487, A091945, A295088.

Sequence in context: A131154 A130994 A266405 * A306010 A162375 A370793

Adjacent sequences: A295084 A295085 A295086 * A295088 A295089 A295090

Keyword

nonn

Author

Rémy Sigrist, Nov 14 2017

Extensions

Formula adapted after change in A091945 by Rémy Sigrist, Dec 07 2022

Status

approved