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 A246344 a(0) = 16, after which, if a(n-1) = product_{k >= 1} (p_k)^(c_k), then a(n) = (1/2) * (1 + product_{k >= 1} (p_{k+1})^(c_k)), where p_k indicates the k-th prime, A000040(k). 5
 16, 41, 22, 20, 32, 122, 101, 52, 77, 72, 338, 434, 611, 451, 280, 1040, 4820, 7907, 3960, 30713, 15364, 22577, 12154, 9791, 4902, 8108, 9131, 5815, 4099, 2056, 3551, 2095, 1474, 1385, 984, 2903, 1455, 1768, 4361, 5869, 2940, 19058, 18845, 13227, 11053, 8707, 4357, 2182, 1640, 4064, 15917, 9432, 46238 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS Iterates of A048673 starting from value 16. Either this sequence is actually part of the cycle containing 12 (see A246342) or 16 is the smallest member of this cycle (regardless of whether this cycle is finite or infinite), which follows because all numbers 1 .. 11 are in finite cycles, and also 13 and 14 are in closed cycles and 15 is in the cycle of 12. LINKS Antti Karttunen, Table of n, a(n) for n = 0..1001 FORMULA a(0) = 16, and for n >= 1, a(n) = A048673(a(n-1)). EXAMPLE Start with a(0) = 16; then after each new term is obtained by replacing each prime factor of the previous term with the next prime, to whose product is added one before it is halved: 16 = 2^4 = p_1^4 -> ((p_2^4)+1)/2 = (3^4 + 1)/2 = (81+1)/2 = 41, thus a(1) = 41. 41 = p_13 -> ((p_14)+1)/2 = (43+1)/2 = 22, thus a(2) = 22. PROG (PARI) default(primelimit, 2^30); A003961(n) = my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); \\ Using code of Michel Marcus A048673(n) = (A003961(n)+1)/2; k = 16; for(n=0, 1001, write("b246344.txt", n, " ", k) ; k = A048673(k)); (Scheme, with memoization-macro definec) (definec (A246344 n) (if (zero? n) 16 (A048673 (A246344 (- n 1))))) CROSSREFS A246345 gives the terms of the same cycle when going to the opposite direction from 16. Cf. A048673, A064216, A246342, A246343. Cf. also A246281, A246282, A246351, A246352, A246361, A246362, A246371, A246372. Sequence in context: A174081 A230802 A100958 * A044093 A044474 A188861 Adjacent sequences: A246341 A246342 A246343 * A246345 A246346 A246347 KEYWORD nonn AUTHOR Antti Karttunen, Aug 24 2014 STATUS approved

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Last modified August 6 18:55 EDT 2024. Contains 374981 sequences. (Running on oeis4.)