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 A349877 a(n) is the number of times the map x -> A353314(x) needs to be applied to n to reach a multiple of 3, or -1 if the trajectory never reaches a multiple of 3. 5
 0, 2, 14, 0, 1, 13, 0, 4, 1, 0, 12, 3, 0, 1, 3, 0, 4, 1, 0, 11, 2, 0, 1, 2, 0, 2, 1, 0, 2, 3, 0, 1, 3, 0, 10, 1, 0, 4, 5, 0, 1, 7, 0, 3, 1, 0, 3, 2, 0, 1, 2, 0, 2, 1, 0, 2, 4, 0, 1, 9, 0, 3, 1, 0, 3, 4, 0, 1, 5, 0, 6, 1, 0, 4, 2, 0, 1, 2, 0, 2, 1, 0, 2, 7, 0, 1, 4, 0, 6, 1, 0, 6, 3, 0, 1, 3, 0, 5, 1, 0, 8, 2, 0 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Equally, number of iterations of A353313 needed to reach a multiple of 3, or -1 if no multiple of 3 is ever reached. - Antti Karttunen, Apr 14 2022 LINKS Antti Karttunen, Table of n, a(n) for n = 0..19683 FORMULA From Antti Karttunen, Apr 14 2022: (Start) If A010872(n) = 0 then a(n) = 0, otherwise a(n) = 1 + a(A353314(n)). a(n) < A353311(n) for all n. (End) EXAMPLE a(1) = 2 : 1 -> 4 -> 9 (as it takes two applications of A353314 to reach a multiple of three), a(2) = 14 : 2 -> 5 -> 10 -> 19 -> 34 -> 59 -> 100 -> 169 -> 284 -> 475 -> 794 -> 1325 -> 2210 -> 3685 -> 6144 a(3) = 0 : 3 (as the starting point 3 is already a multiple of 3). a(4) = 1 : 4 -> 9 a(7) = 4 : 7 -> 14 -> 25 -> 44 -> 75. PROG (Python) import itertools def f(n): for i in itertools.count(): quot, rem = divmod(n, 3) if rem == 0: return i n = (5 * quot) + rem + 3 (PARI) A353314(n) = { my(r=(n%3)); if(!r, n, ((5*((n-r)/3)) + r + 3)); }; A349877(n) = { my(k=0); while(n%3, k++; n = A353314(n)); (k); }; \\ Antti Karttunen, Apr 14 2022 CROSSREFS Cf. A010872, A349876, A353311, A353313. Sequence in context: A219221 A249510 A324219 * A196815 A260120 A221234 Adjacent sequences: A349874 A349875 A349876 * A349878 A349879 A349880 KEYWORD nonn,easy AUTHOR Nicholas Drozd, Dec 03 2021 EXTENSIONS Definition corrected and more terms from Antti Karttunen, Apr 14 2022 STATUS approved

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Last modified December 9 02:18 EST 2023. Contains 367681 sequences. (Running on oeis4.)