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The least i for which A163355^n(i) is not equal to i, 0 if no such i exists, i.e., when A163355^n = A001477.
6

%I #11 Nov 22 2023 05:04:18

%S 0,2,4,2,4,2,24,2,4,2,4,2,33,2,4,2,4,2,24,2,4,2,4,2,76,2,4,2,4,2,24,2,

%T 4,2,4,2,33,2,4,2,4,2,24,2,4,2,4,2,76,2,4,2,4,2,24,2,4,2,4,2,33,2,4,2,

%U 4,2,24,2,4,2,4,2,390,2,4,2,4,2,24,2,4,2,4,2,33,2,4,2,4,2,24,2,4,2,4

%N The least i for which A163355^n(i) is not equal to i, 0 if no such i exists, i.e., when A163355^n = A001477.

%C A163355^n means n-fold application of A163355, i.e., A163355^2 = A163905, A163355^3 = A163915. By convention A163355^0 = A001477.

%H A. Karttunen, <a href="/A163894/b163894.txt">Table of n, a(n) for n = 0..4095</a>

%p A163894 := proc(n)

%p local i,a355,a,itr ;

%p if n = 0 then

%p return 0 ;

%p end if;

%p a := 0 ;

%p for i from 0 do

%p a355 := A163355(i) ;

%p for itr from 2 to n do

%p a355 := A163355(a355) ;

%p end do:

%p if a355 <> i then

%p return i ;

%p end if;

%p end do:

%p end proc:

%p seq(A163894(n),n=0..100) ; # _R. J. Mathar_, Nov 22 2023

%o (MIT Scheme:)

%o (define (A163894 n) (if (zero? n) 0 (let loop ((i 1) (n-th_power (compose-fun-to-n-th-power a163355 n))) (cond ((not (= i (n-th_power i))) i) (else (loop (1+ i) n-th_power))))))

%o (define (compose-fun-to-n-th-power fun n) (cond ((zero? n) (lambda (x) x)) (else (lambda (x) (fun ((compose-fun-to-n-th-power fun (- n 1)) x))))))

%Y See A163890, A163895, A163896.

%K nonn

%O 0,2

%A _Antti Karttunen_, Sep 19 2009