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

0,1

Comments

Iterates of A064216 starting from value 16.

See also the comments in A246344.

Links

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

Formula

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

Example

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.

Mathematica

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

Prog

(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)))))

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.

Sequence in context: A064803 A220762 A353597 * A054314 A222545 A115278

Adjacent sequences: A246342 A246343 A246344 * A246346 A246347 A246348

Keyword

nonn

Author

Antti Karttunen, Aug 24 2014

Status

approved