R, 57 55 50 bytes

\(n)cbind(a<-1:n+1,b<-n+3-a%x%!!a)[order(a^b)[n],]

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Returns the \$n^\text{th}\$ value.

-2 bytes thanks to pajonk, then -4 more bytes thanks to pajonk.

R, 57 55 50 46 bytes

\(n)cbind(a<-n:1+1,b<-a%x%!!a)[order(a^b)[n],]

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Returns the \$n^\text{th}\$ value.

-2 bytes thanks to pajonk, then -4 more bytes thanks to pajonk. -1 byte thanks to Dominic van Essen.

R, 57 55 bytes

\(n)cbind(a<-1:n+1,b<-a%x%!!a)[order(a^b,rep(a,n))[n],]

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Returns the \$n^\text{th}\$ value.

-2 bytes thanks to pajonk.

R, 57 55 50 bytes

\(n)cbind(a<-1:n+1,b<-n+3-a%x%!!a)[order(a^b)[n],]

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Returns the \$n^\text{th}\$ value.

-2 bytes thanks to pajonk, then -4 more bytes thanks to pajonk.

R, 57 bytes

\(n)cbind(a<-1:n+1,b<-a%x%!!1:n)[order(a^b,rep(a,n))[n],]

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Returns the \$n^\text{th}\$ value.

R, 57 55 bytes

\(n)cbind(a<-1:n+1,b<-a%x%!!a)[order(a^b,rep(a,n))[n],]

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Returns the \$n^\text{th}\$ value.

-2 bytes thanks to pajonk.