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A246343 a(0) = 12, after which, if (2*a(n-1)) - 1 = product_{k >= 1} (p_k)^(c_k) then a(n) = product_{k >= 1} (p_{k-1})^(c_k), where p_k indicates the k-th prime, A000040(k).

%I A246343 #10 Aug 26 2014 01:24:59
%S A246343 12,19,31,59,44,46,55,107,134,166,317,398,282,557,470,622,763,531,
%T A246343 1051,1267,1807,3607,7211,4522,9041,3700,3725,3982,7951,15889,30053,
%U A246343 24018,24189,34535,14630,12916,21769,27599,24524,32678,26094,43073,34446,68881,116479,143359,275221,550439,667462,1051489
%N A246343 a(0) = 12, after which, if (2*a(n-1)) - 1 = product_{k >= 1} (p_k)^(c_k) then a(n) = product_{k >= 1} (p_{k-1})^(c_k), where p_k indicates the k-th prime, A000040(k).
%C A246343 Iterates of A064216 starting from value 12.
%C A246343 All numbers from 1 to 11 are in finite cycles of A048673/A064216, thus 12 is the smallest number in this cycle, regardless of whether it is infinite or finite.
%H A246343 Antti Karttunen, <a href="/A246343/b246343.txt">Table of n, a(n) for n = 0..1001</a>
%F A246343 a(0) = 12, a(n) = A064216(a(n-1)).
%e A246343 Start with a(0) = 12; then after each new term is obtained by doubling the previous term, from which one is subtracted, after which each prime factor is replaced with the previous prime:
%e A246343 12 -> ((2*12)-1) = 23 = p_9, and p_8 = 19, thus a(1) = 19.
%e A246343 19 -> ((2*19)-1) = 37 = p_12, and p_11 = 31, thus a(2) = 31.
%e A246343 31 -> ((2*31)-1) = 61 = p_18, and p_17 = 59, thus a(3) = 59.
%e A246343 59 -> ((2*59)-1) = 117 = 3*3*13 = p_2 * p_2 * p_6, and p_1 * p_1 * p_5 = 2*2*11 = 44, thus a(4) = 44.
%o A246343 (PARI)
%o A246343 default(primelimit, 2^30);
%o A246343 A064989(n) = {my(f); f = factor(n); if((n>1 && f[1,1]==2), f[1,2] = 0); for (i=1, #f~, f[i,1] = precprime(f[i,1]-1)); factorback(f)};
%o A246343 A064216(n) = A064989((2*n)-1);
%o A246343 k = 12; for(n=0, 1001, write("b246343.txt", n, " ", k); k = A064216(k));
%o A246343 (Scheme, with memoization-macro definec)
%o A246343 (definec (A246343 n) (if (zero? n) 12 (A064216 (A246343 (- n 1)))))
%Y A246343 A246342 gives the terms of the same cycle when going to the opposite direction from 12.
%Y A246343 Cf. A048673, A064216, A246344, A246345.
%Y A246343 Cf. also A246281, A246282, A246351, A246352, A246361, A246362, A246371, A246372.
%K A246343 nonn
%O A246343 0,1
%A A246343 _Antti Karttunen_, Aug 24 2014