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%I #10 Apr 04 2015 15:03:10
%S 16,29,34,61,49,89,106,199,389,310,617,524,694,1207,1921,3097,3899,
%T 4142,3374,3674,4234,8461,16903,20211,37841,22408,26853,26391,48031,
%U 68605,137201,81272,108334,137809,266737,512627,347932,497005,982081,1942279,3855031,5292209
%N a(0) = 16, 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 Iterates of A064216 starting from value 16.
%C See also the comments in A246344.
%H Antti Karttunen, <a href="/A246345/b246345.txt">Table of n, a(n) for n = 0..1001</a>
%F a(0) = 16, a(n) = A064216(a(n-1)).
%e Start with a(0) = 16; 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 16 -> ((2*16)-1) = 31 = p_1, and p_10 = 29, thus a(1) = 29.
%e 29 -> ((2*29)-1) = 57 = 3*19 = p_2 * p_8, and p_1 * p_7 = 2*17 = 34, thus a(2) = 34.
%t nxt[n_]:=Times@@(NextPrime[#,-1]&/@(Flatten[Table[#[[1]],{#[[2]]}]&/@ FactorInteger[2 n-1]])); NestList[nxt,16,50] (* _Harvey P. Dale_, Apr 04 2015 *)
%o (PARI)
%o default(primelimit, 2^30);
%o 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 A064216(n) = A064989((2*n)-1);
%o k = 16; for(n=0, 1001, write("b246345.txt", n, " ", k); k = A064216(k));
%o (Scheme, with memoization-macro definec)
%o (definec (A246345 n) (if (zero? n) 16 (A064216 (A246345 (- n 1)))))
%Y A246344 gives the terms of the same cycle when going to the opposite direction from 16.
%Y Cf. A048673, A064216, A246342, A246343.
%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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