A275114 Primes p for which the sum of the numbers in the Collatz iteration (A033493) of p is a prime.

2, 67, 149, 163, 229, 359, 373, 401, 571, 719, 727, 827, 919, 941, 1031, 1049, 1129, 1153, 1201, 1283, 1307, 1319, 1433, 1453, 1627, 1637, 1987, 2017, 2089, 2137, 2237, 2267, 2281, 2351, 2543, 2617, 2731, 2819, 2851, 2861, 2927, 2969, 3191, 3253, 3581, 3671, 3719

Offset

1,1

Comments

Primes p such that A033493(p) is a prime.

Prime terms from A225748.

Links

Table of n, a(n) for n=1..47.

Eric Weisstein's World of Mathematics, Collatz Problem

Wikipedia, Collatz conjecture

Example

Prime 67 with Collatz trajectory (67, 202, 101, 304, 152, 76, 38, 19, 58, 29, 88, 44, 22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1) is a term because A033493(67) = 1459 (prime).

Mathematica

Select[Prime@ Range@ 540, PrimeQ[Total@ FixedPointList[Which[# == 1, 1, EvenQ@ #, #/2, True, 3 # + 1] &, #] - 1] &] (* Michael De Vlieger, Jul 17 2016, after Alonso del Arte at A033493 *)

Prog

(Magma) [n: n in [1..4000] | IsPrime(&+[k eq 1 select n else IsOdd(Self(k-1)) and not IsOne(Self(k-1)) select 3*Self(k-1)+1 else Self(k-1) div 2: k in [1..5*n]]) and IsPrime(n)]

Crossrefs

Cf. A033493, A225748.

Sequence in context: A065721 A030472 A106998 * A217599 A107214 A371509

Adjacent sequences: A275111 A275112 A275113 * A275115 A275116 A275117

Keyword

nonn

Author

Jaroslav Krizek, Jul 17 2016

Status

approved