A355711 - OEIS

%I #9 Jul 19 2022 07:27:28

%S 33,85,93,145,213,265,393,445,453,475,505,633,685,753,805,813,865,933,

%T 985,993,1045,1113,1165,1293,1345,1353,1405,1430,1533,1585,1624,1653,

%U 1705,1713,1765,1833,1885,1893,1945,2013,2065,2193,2245,2253,2275,2305,2433,2485

%N Starts of runs of 3 consecutive numbers with the same number of 5-smooth divisors.

%C Numbers k such that A355583(k) = A355583(k+1) = A355583(k+2).

%H Amiram Eldar, <a href="/A355711/b355711.txt">Table of n, a(n) for n = 1..10000</a>

%e 33 is a term since A355583(33) = A355583(34) = A355583(35) = 2.

%t f[n_] := Times @@ (1 + IntegerExponent[n, {2, 3, 5}]); s = {}; m = 3; fs = f /@ Range[m]; Do[If[Equal @@ fs, AppendTo[s, n - m]]; fs = Rest @ AppendTo[fs, f[n]], {n, m + 1, 2500}]; s

%o (PARI) s(n) = (valuation(n, 2) + 1) * (valuation(n, 3) + 1) * (valuation(n, 5) + 1);

%o s1 = s(1); s2 = s(2); for(k = 3, 2500, s3 = s(k); if(s1 == s2 && s2 == s3, print1(k-2,", ")); s1 = s2; s2 = s3);

%Y Cf. A355583.

%Y Subsequence of A355710.

%Y A355712 is a subsequence.

%Y Similar sequences: A005238, A006073, A045939, A332313, A332387.

%K nonn

%O 1,1

%A _Amiram Eldar_, Jul 15 2022