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

%I A275114 #15 Aug 18 2025 15:43:09
%S A275114 2,67,149,163,229,359,373,401,571,719,727,827,919,941,1031,1049,1129,
%T A275114 1153,1201,1283,1307,1319,1433,1453,1627,1637,1987,2017,2089,2137,
%U A275114 2237,2267,2281,2351,2543,2617,2731,2819,2851,2861,2927,2969,3191,3253,3581,3671,3719
%N A275114 Primes p for which the sum of the numbers in the Collatz iteration (A033493) of p is a prime.
%C A275114 Primes p such that A033493(p) is a prime.
%C A275114 Prime terms from A225748.
%H A275114 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/CollatzProblem.html">Collatz Problem</a>
%H A275114 Wikipedia, <a href="http://en.wikipedia.org/wiki/Collatz_conjecture">Collatz conjecture</a>
%e A275114 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).
%t A275114 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 *)
%o A275114 (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)];
%Y A275114 Cf. A033493, A225748.
%K A275114 nonn
%O A275114 1,1
%A A275114 _Jaroslav Krizek_, Jul 17 2016