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%I #15 Aug 26 2014 01:20:27
%S 12,23,15,18,38,35,39,43,24,68,86,71,37,21,28,50,74,62,56,149,76,104,
%T 230,305,235,186,278,224,1337,1062,2288,8951,4482,16688,67271,33637,
%U 16821,66688,571901,338059,181516,258260,455900,1180337,1080207,1817863,1157487,984558,1230848,53764115
%N a(0) = 12, 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).
%C Iterates of A048673 starting from value 12.
%C All numbers 1 .. 11 are in finite cycles of A048673/A064216, thus 12 is the smallest number in this cycle, regardless of whether the cycle is infinite or finite.
%C This sequence soon reaches much larger values than the corresponding A246343 (iterating the same cycle in the other direction). However, with the corresponding sequences starting from 16 (A246344 & A246345), there is no such pronounced difference, and with them the bias is actually the other way.
%H Antti Karttunen, <a href="/A246342/b246342.txt">Table of n, a(n) for n = 0..1001</a>
%F a(0) = 12, and for n >= 1, a(n) = A048673(a(n-1)).
%e Start with a(0) = 12; thereafter each new term is obtained by replacing each prime factor of the previous term with the next prime, to whose product 1 is added before it is halved:
%e 12 = 2^2 * 3 = p_1^2 * p_2 -> ((p_2^2 * p_3)+1)/2 = ((9*5)+1)/2 = 23, thus a(1) = 23.
%e 23 = p_9 -> (p_10 + 1)/2 = (29+1)/2 = 15, thus a(2) = 15.
%o (PARI)
%o default(primelimit, 2^30);
%o 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_
%o A048673(n) = (A003961(n)+1)/2;
%o k = 12; for(n=0, 1001, write("b246342.txt", n, " ", k) ; k = A048673(k));
%o (Scheme, with memoization-macro definec)
%o (definec (A246342 n) (if (zero? n) 12 (A048673 (A246342 (- n 1)))))
%Y A246343 gives the terms of the same cycle when going in the opposite direction from 12.
%Y Cf. A048673, A064216, A246344, A246345.
%Y Cf. also A246281, A246282, A246351, A246352, A246361, A246362, A246371, A246372.
%K nonn
%O 0,1
%A _Antti Karttunen_, Aug 24 2014
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