A307485 -id:A307485 - cp's OEIS frontend

A307612 Partial sums of the permutation A307485: one odd, two even, four odd, eight even, etc.

0, 1, 3, 7, 10, 15, 22, 31, 37, 45, 55, 67, 81, 97, 115, 135, 146, 159, 174, 191, 210, 231, 254, 279, 306, 335, 366, 399, 434, 471, 510, 551, 573, 597, 623, 651, 681, 713, 747, 783, 821, 861, 903, 947, 993, 1041, 1091, 1143, 1197, 1253, 1311, 1371, 1433, 1497, 1563, 1631, 1701, 1773, 1847

Offset: 0

M. F. Hasler, Apr 18 2019

nonn

Orap Andrew a.k.a. Dalgerok, Codeforces Round #553 - C. Problem for Nazar, on Codeforces.com, April 2019
OEIS Index to sequences related to permutations of the integers.

Cf. A307485 (the "1 odd, 2 even, 4 odd..." permutation), A307612 (partial sums thereof).

PARI
```
A307612(n,s=1,S,t,i=1)=until(n
				
```

A307613 Inverse of the permutation A307485: one odd, two even, four odd, eight even, etc; extended with a(0) = 0.

Original entry on oeis.org

0, 1, 2, 4, 3, 5, 8, 6, 9, 7, 10, 16, 11, 17, 12, 18, 13, 19, 14, 20, 15, 21, 32, 22, 33, 23, 34, 24, 35, 25, 36, 26, 37, 27, 38, 28, 39, 29, 40, 30, 41, 31, 42, 64, 43, 65, 44, 66, 45, 67, 46, 68, 47, 69, 48, 70, 49, 71, 50, 72, 51, 73, 52, 74, 53, 75, 54, 76, 55, 77

Offset: 0

M. F. Hasler, Apr 18 2019

nonn

See A307485 for further information, motivation & references.

Also, a(n) is the smallest k not yet in the sequence such that bitxor(k,a(n-1)) >= a(n-1). - Giorgos Kalogeropoulos, May 31 2019

			  Index n : 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, ...
A307485(n): 0, 1, 2, 4, 3, 5, 7, 9, 6, 8, ...
This sequence, the inverse permutation, is obtained by reading the above "from bottom to top", i.e., find the index in 2nd row, return the number above it: e.g., a(3) = 4, a(4) = 3, a(5) = 5, a(6) = 8, a(7) = 6, etc.

OEIS' Index to sequences related to permutations of the integers.

Cf. A307485 (inverse permutation), A307612 (partial sums thereof).
Cf. A103889 (odd & even swapped), A004442 (pairs reversed: n + (-1)^n).
Odd numbers: A005408. Even numbers: A005843.
Cf. A233275 (different permutation based on entangling odd & even numbers).

a[1]=1; a[n_] := a[n] = (t=1; While[BitXor[a[n-1],t] < a[n-1] || MemberQ[Array[a, n-1], t], t++]; t)
Join[{0}, Table[a[k], {k,100}]]  (* Giorgos Kalogeropoulos, May 31 2019 *)

my(A=apply(A307485,[1..99]), B=vecsort(A,,1)); for(i=1,#B,A[B[i]]==i||return(A307613=B[1..i-1]))

cp's OEIS Frontend

A307612 Partial sums of the permutation A307485: one odd, two even, four odd, eight even, etc.

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