OFFSET
1,1
COMMENTS
The next term, surprisingly, is the 2743-digit (53 * 2^9107 - 1)/3. See A177331 for additional prime numbers, besides 3, that are not in the Collatz iteration of any prime number.
EXAMPLE
a(4) = 37 because the Collatz iteration of 37 is {37, 112, 56, 28, 14, 7, 22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1}, which shows that 7 is the next prime after 37.
MATHEMATICA
Table[p = Prime[n]; If[p == 3, q = 0, k = 1; While[q = (p*2^k - 1)/3; k < 10000 && ! PrimeQ[q], k++]]; q, {n, 15}]
CROSSREFS
KEYWORD
nonn
AUTHOR
T. D. Noe, May 22 2013
STATUS
approved