cp's OEIS Frontend

A375093 Numbers for which the number of squares in their Collatz trajectory sets a new record.

%I A375093 #6 Aug 03 2024 17:58:35
%S A375093 1,3,9,27,133,315,747,2799,14175,287061,530079,3061987,18371925,
%T A375093 73487701,195967203,1175803221
%N A375093 Numbers for which the number of squares in their Collatz trajectory sets a new record.
%e A375093 a(1) = 1: the square 1 contained in every trajectory at the end,
%e A375093 a(2) = 3: 3 squares in 3 -> 10 -> 5 -> 4^2 -> 8 -> 2^2 -> 2 -> 1^2,
%e A375093 a(3) = 9: 4 squares in 3^2 -> 28 -> ... -> 10 -> as above,
%e A375093 a(4) = 27: the famous long trajectory A008884 includes the 5 squares 22^2, 11^2, 4^2, 2^2, 1^2,
%e A375093 a(5) = 133: 6 squares in 133 -> 20^2 -> 200 -> 10^2 -> 50 -> 5^2 -> ... -> 4^2, 2^2, 1^2,
%e A375093 a(6) = 315: 7 squares in 315 -> 946 -> ... -> 533 -> 40^2 -> 800 -> 20^2 -> as above,
%e A375093 a(7) = 747: 9 squares in 747 -> 2242 -> 1121 -> 58^2 -> 1682 -> 29^2 -> ... -> 1066 -> 533 -> as above.
%o A375093 (PARI) nextc(x) = if (x%2==0, x\2, 3*x+1);
%o A375093 a375093(upto=600000) = {my(m=0); for (k=1, upto, np=issquare(k); j=k; while (j>1, j=nextc(j); if (issquare(j), np++)); if (np>m, m=np; print1(k,", ")))}
%Y A375093 Cf. A000290, A006877, A008884, A078373.
%K A375093 nonn,more
%O A375093 1,2
%A A375093 _Hugo Pfoertner_, Jul 29 2024