OFFSET
0,1
COMMENTS
LINKS
Antti Karttunen, Table of n, a(n) for n = 0..1001
FORMULA
a(0) = 12, and for n >= 1, a(n) = A048673(a(n-1)).
EXAMPLE
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:
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.
23 = p_9 -> (p_10 + 1)/2 = (29+1)/2 = 15, thus a(2) = 15.
PROG
(PARI)
default(primelimit, 2^30);
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
k = 12; for(n=0, 1001, write("b246342.txt", n, " ", k) ; k = A048673(k));
(Scheme, with memoization-macro definec)
CROSSREFS
A246343 gives the terms of the same cycle when going in the opposite direction from 12.
KEYWORD
nonn
AUTHOR
Antti Karttunen, Aug 24 2014
STATUS
approved