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 A322418 Least k > 0 such that A014221(k) == A014221(k+1) mod n. 2
 1, 1, 2, 2, 3, 2, 3, 3, 3, 3, 4, 2, 3, 3, 3, 3, 4, 3, 4, 3, 3, 4, 5, 3, 4, 3, 4, 3, 4, 3, 4, 4, 4, 4, 3, 3, 4, 4, 3, 3, 4, 3, 4, 4, 3, 5, 6, 3, 4, 4, 4, 3, 4, 4, 4, 3, 4, 4, 5, 3, 4, 4, 3, 4, 3, 4, 5, 4, 5, 3, 4, 3, 4, 4, 4, 4, 4, 3, 4, 3, 5, 4, 5, 3, 4, 4, 4, 4, 5, 3 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS For any fixed integer n > 0, the sequence 2 mod n, 2^2 mod n, 2^2^2 mod n, that is, the sequence {A014221(i) mod n} for i >= 1 is eventually constant. a(n) is the least index k such that A014221(k) mod n equals this constant. A038081(k+1) is the largest n such that a(n) = k. LINKS USAMO, Problem 3, 1991. FORMULA a(n) <= A003434(n). a(n) <= a(A000010(n)) + 1. If A014221(k) == b(k) mod eulerphi(n), 0 < b(k) <= eulerphi(n), then a(n) is the least m > 0 such that 2^b(m-1) == 2^b(m) mod n. EXAMPLE 2, 4, 16, ... mod 6 equal 2, 4, 4, ..., so A014221(k) mod 6 = 4 for all k >= 2, hence a(6) = 2. PROG (PARI) a(n) = {c=0; k=1; x=1; d=n; while(k==1, z=x; y=1; b=1; while(z>0, while(y

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Last modified August 9 11:08 EDT 2020. Contains 336323 sequences. (Running on oeis4.)