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

Author

Jaroslav Krizek, Jul 17 2016

Keywords

• nonn

Comments

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

Prime terms from A225748.

Examples

			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).
		

Links

• Eric Weisstein's World of Mathematics, Collatz Problem
• Wikipedia, Collatz conjecture

Crossrefs

Cf. A033493, A225748.

Programs

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)];

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 *)