A372060 a(n) = smallest k such that A252867(k) = n, or -1 if no such k exists.

0, 1, 2, 6, 5, 3, 9, 13, 12, 10, 4, 18, 7, 23, 16, 25, 22, 8, 11, 20, 28, 35, 32, 41, 14, 38, 43, 59, 30, 56, 53, 75, 17, 15, 27, 29, 19, 66, 39, 70, 21, 33, 36, 85, 49, 68, 51, 95, 24, 64, 45, 79, 47, 104, 98, 110, 62, 93, 73, 115, 106, 113, 108, 154, 42, 31, 34, 48, 37, 44

Offset

0,3

Comments

Both A252867 and this sequence are conjectured to be permutations of the nonnegative integers, in which case they are inverses of each other.

Links

Michael S. Branicky, Table of n, a(n) for n = 0..100000 (terms 0..9999 from N. J. A. Sloane)

Maple

A372060 := proc(n)
    local i;
    for i from 0 do
        if A252867(i) = n then
            return i ;
        end if;
    end do:
end proc:
for n from 0 do
    printf("%d %d\n", n, A372060(n)) ; # b-style output
end do: # R. J. Mathar, May 02 2024

Mathematica

kmax = 1000;
b[n_] := b[n] = Module[{k}, If[n < 3, n, For[k = 3, True, k++, If[FreeQ[Array[b, n - 1], k], If[BitAnd[k, b[n - 2]] >= 1 && BitAnd[k, b[n - 1]] == 0, Return[k]]]]]];
a[n_] := Module[{k}, For[k = 0, k <= kmax, k++, If[b[k] == n, Return[k]]]] /. Null -> -1;
Table[a[n], {n, 0, 100}] (* Jean-François Alcover, May 10 2024 *)

Prog

(Python)
def A372060(n):
    if n<3: return n
    l1, l2, s, b, k = 2, 1, 3, set(), 3
    while True:
        for i in count(s):
            if not (i in b or i & l1) and i & l2:
                if i == n: return k
                k += 1
                l2, l1 = l1, i
                b.add(i)
                while s in b:
                    b.remove(s)
                    s += 1
                break # Chai Wah Wu, May 02 2024

Crossrefs

Cf. A252867.

Sequence in context: A157890 A329932 A359858 * A198821 A171897 A105029

Adjacent sequences: A372057 A372058 A372059 * A372061 A372062 A372063

Keyword

nonn,changed

Author

N. J. A. Sloane, May 01 2024

Status

approved