A258251 Numbers n for which there exists a fixed point in the Collatz (3x+1) trajectory of n.
1, 4, 5, 9, 12, 13, 22, 23, 24, 26, 32, 33, 36, 37, 38, 49, 50, 51, 56, 58, 60, 61, 72, 74, 78, 79, 80, 86, 87, 105, 123, 124, 125, 126, 127, 130, 131, 132, 133, 134, 136, 138, 140, 141, 153, 156, 157, 158, 160, 168, 170, 192, 196, 197, 198, 200, 202, 204, 205, 206, 207, 217, 224, 232, 233, 234, 241, 246, 247, 249
Offset: 1
Keywords
Examples
For n = 5, the trajectory is T(5) = [5, 16, 8, 4, 2, 1]. Since the fourth term in this sequence is 4, 5 has a fixed point. So 5 is a member of this sequence. For n = 6, the trajectory is T(6) = [6, 3, 10, 5, 16, 8, 4, 2, 1]. Here, there is no fixed point and so, 6 is not a member of this sequence.
Programs
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PARI
Tvect(n)=v=[n]; while(n!=1, if(n%2, k=3*n+1; v=concat(v, k); n=k); if(!(n%2), k=n/2; v=concat(v, k); n=k)); v m=1; while(m<10^3, d=Tvect(m); c=0; for(i=1, #d, if(d[i]==i, print1(m, ", "); break)); m++)
Comments