A256992 Position of n in either of the complementary sequences, A005187 or A055938: a(n) = A213714(n) + A234017(n).

1, 1, 2, 3, 2, 3, 4, 5, 4, 6, 7, 5, 6, 7, 8, 9, 8, 10, 11, 9, 10, 12, 13, 11, 14, 15, 12, 13, 14, 15, 16, 17, 16, 18, 19, 17, 18, 20, 21, 19, 22, 23, 20, 21, 22, 24, 25, 23, 26, 27, 24, 25, 28, 29, 26, 30, 31, 27, 28, 29, 30, 31, 32, 33, 32, 34, 35, 33, 34, 36, 37, 35, 38, 39, 36, 37, 38, 40, 41, 39, 42, 43, 40, 41, 44, 45, 42

Offset

1,3

Comments

In other words, if n = A005187(k) for some k >= 1, then a(n) = k, otherwise it must be that n = A055938(h) for some h, and then a(n) = h.

Each n occurs exactly twice, first at a(A005187(n)), then at a(A055938(n)). Cf. also A257126.

When iterating a(n), a(a(n)), a(a(a(n))), etc, A256993(n) gives the number of steps to reach one, from any starting value n >= 1.

Links

Antti Karttunen, Table of n, a(n) for n = 1..16384

Formula

a(n) = A213714(n) + A234017(n).

a(n) = A256991(n) + A079559(n).

If A079559(n) = 1, a(n) = A213714(n), otherwise a(n) = A234017(n).

Mathematica

With[{nn = 92}, Function[{g, h}, Flatten@ Table[If[MemberQ[g, n], First@ Position[g, n] - 1, First@ Position[h, n]], {n, Min[Length /@ {g, h}]}]] @@ {Table[2 n - DigitCount[2 n, 2, 1], {n, 0, nn}], Complement[Range@ Last@ #, #] &@ Table[IntegerExponent[(2 n)!, 2], {n, 0, nn}]} ] (* Michael De Vlieger, Dec 12 2016, after Harvey P. Dale at A005187 and Jean-François Alcover at A055938 *)

Prog

(Scheme)
(define (A256992 n) (+ (A213714 n) (A234017 n)))
(define (A256992 n) (if (not (zero? (A079559 n))) (A213714 n) (A234017 n)))

Crossrefs

Cf. A005187, A055938, A079559, A213714, A234017.

Cf. also A256991 (variant), A256993, A257126.

Sequence in context: A106249 A110516 A187180 * A261323 A134986 A336860

Adjacent sequences: A256989 A256990 A256991 * A256993 A256994 A256995

Keyword

nonn

Author

Antti Karttunen, Apr 15 2015

Status

approved