



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
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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 JeanFrançois 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 A216209
Adjacent sequences: A256989 A256990 A256991 * A256993 A256994 A256995


KEYWORD

nonn


AUTHOR

Antti Karttunen, Apr 15 2015


STATUS

approved



