This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A276202 #33 Mar 29 2025 18:09:19
%S A276202 1,4,3,6,11,7,14,9,25,33,59,57,39,135,191,127,123,159,219,379,251,167,
%T A276202 223,111,793,263,175,466,103,137,183,91,121,107,71,47,31,41,27,97,145,
%U A276202 129,171,231,235,553,411,487,327,649,703,763,1519,1215,1471,1071
%N A276202 Smallest integer k such that the number of semiprimes in {k, f(k), f(f(k)), ..., 1} is equal to n, where f is the Collatz function.
%C A276202 Smallest k such that A275866(k) is equal to n.
%C A276202 Conjecture: a(n) exists for any n.
%H A276202 Michel Lagneau, <a href="/A276202/b276202.txt">Table of n, a(n) for n = 0..100</a>
%H A276202 <a href="/index/3#3x1">Index entries for sequences related to 3x+1 (or Collatz) problem</a>
%e A276202 a(5)=7 because the trajectory of 7 is 7 -> 22 -> 11 -> 34 -> 17 -> 52 -> 26 -> 13 -> 40 -> 20 -> 10 -> 5 -> 16 -> 8 -> 4 -> 2 -> 1 and the 5 semiprimes of this trajectory are 22, 34, 26, 10 and 4.
%t A276202 f[n_]:=n/2/; Mod[n, 2]==0; f[n_]:=3 n+1/; Mod[n, 2]==1; g[n_]:=Module[{i, p}, i=n; p=0; While[i>1, If[PrimeOmega[i]==2, p=p+1]; i=f[i]]; p]; Do[k=1; While[g[k]!=m, k++]; Print[m, " ", k], {m, 0, 53}]
%t A276202 nsp[n_]:={n,Count[NestWhileList[If[EvenQ[#],#/2,3#+1]&,n,#>1&],_?(PrimeOmega[#]==2&)]}; Table[SelectFirst[nsp/@Range[2000],#[[2]] == n&],{n,0,59}][[;;,1]] (* _Harvey P. Dale_, Mar 29 2025 *)
%Y A276202 Cf. A006577, A275866.
%K A276202 nonn
%O A276202 0,2
%A A276202 _Michel Lagneau_, Aug 29 2016