A246345 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).

16, 29, 34, 61, 49, 89, 106, 199, 389, 310, 617, 524, 694, 1207, 1921, 3097, 3899, 4142, 3374, 3674, 4234, 8461, 16903, 20211, 37841, 22408, 26853, 26391, 48031, 68605, 137201, 81272, 108334, 137809, 266737, 512627, 347932, 497005, 982081, 1942279, 3855031, 5292209

Offset: 0

Author

Antti Karttunen, Aug 24 2014

Keywords

• nonn

Comments

Iterates of A064216 starting from value 16.

See also the comments in A246344.

Examples

			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:
16 -> ((2*16)-1) = 31 = p_1, and p_10 = 29, thus a(1) = 29.
29 -> ((2*29)-1) = 57 = 3*19 = p_2 * p_8, and p_1 * p_7 = 2*17 = 34, thus a(2) = 34.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 0..1001

Crossrefs

A246344 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.

Programs

Mathematica

nxt[n_]:=Times@@(NextPrime[#,-1]&/@(Flatten[Table[#[[1]],{#[[2]]}]&/@ FactorInteger[2 n-1]])); NestList[nxt,16,50] (* Harvey P. Dale, Apr 04 2015 *)

PARI

default(primelimit, 2^30);
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)};
A064216(n) = A064989((2*n)-1);
k = 16; for(n=0, 1001, write("b246345.txt", n, " ", k); k = A064216(k));
(Scheme, with memoization-macro definec)
(definec (A246345 n) (if (zero? n) 16 (A064216 (A246345 (- n 1)))))

Formula

a(0) = 16, a(n) = A064216(a(n-1)).