A225424 Least prime p such that prime(n) is the next prime number in the Collatz (3x+1) iteration of p, or 0 if there is no such prime.

5, 0, 3, 37, 7, 17, 11, 101, 61, 19, 41, 197, 109, 229, 31

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.

Links

Table of n, a(n) for n=1..15.

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

Cf. A070165, A177330, A177331.

Sequence in context: A339457 A300728 A321418 * A202626 A011995 A258754

Adjacent sequences: A225421 A225422 A225423 * A225425 A225426 A225427

Keyword

nonn

Author

T. D. Noe, May 22 2013

Status

approved