A387787 - OEIS

%I #29 Dec 11 2025 17:03:28

%S 3,4,6,7,9,10,14,17,19,22,25,26,27,31,34,38,41,43,46,49,51,55,57,58,

%T 62,63,71,74,81,82,83,86,89,91,94,97,103,105,106,111,118,119,122,129,

%U 134,137,142,145,146,147,158,166,169,175,178,179,185,194,201,202

%N Positive integers k for which the Collatz 3x+1 dropping value (first value < k) is prime.

%C All k = 2*prime (A100484) are terms so the sequence is infinite.

%C A given prime can be the drop value of various different k, as for example 23 is the drop value of k = 27, 31, 46.

%e For k = 3: 3 -> 10 -> 5 -> 16 -> 8 -> 4 -> 2 -> 1. The first term < 3 is 2, which is prime, so 3 is a term.

%e For k = 8: 8 -> 4 -> 2 -> 1. The first term < 8 is 4, which is composite, so 8 is not a term.

%o (Python)

%o from sympy import isprime

%o def T(n):

%o     return n//2 if n % 2 == 0 else 3*n + 1

%o def drop(k):

%o     x = k

%o     while x >= k:

%o         x = T(x)

%o     return x

%o def isok(k):

%o     return isprime(drop(k))

%o (PARI) isok(k) = if (k>1, my(m=k); while(m >= k, m = if (m%2, 3*m+1, m/2)); isprime(m)); \\ _Michel Marcus_, Dec 06 2025

%Y Cf. A100484, A060565, A070165, A006370, A074473.

%K nonn,easy

%O 1,1

%A _Aied Sulaiman_, Dec 04 2025