A116459 - OEIS

%I #12 Sep 11 2024 10:06:56

%S 171,342,427,683,684,854,855,1111,1195,1366,1367,1368,1451,1707,1708,

%T 1710,2390,2732,2734,2736,2902,3414,3415,3416,3420,3755,4203,4271,

%U 4780,4781,5463,5464,5468,5472,5483,5803,5804,6319,6331,6383,6491,6827,6828

%N Numbers k such that A003313(k) = A003313(3*k).

%H Hugo Pfoertner, <a href="/A116459/b116459.txt">Table of n, a(n) for n = 1..10000</a>

%e a(3)=427 because both 427 and 1281=3*427 have associated shortest addition chains of length 12: [1,2,4,8,16,17,34,68,136,137,145,290,427] and [1,2,4,5,10,20,40,80,160,320,640,1280]. This is the third occurrence of such a pair. The first two are (171,513) and (342,1026).

%Y Cf. A115016, A003313 [l(k)], A086878 [l(k)=l(2*k)], A261986 [l(k)=l(4*k)], A116460 [l(k)=l(5*k)], A116461 [l(k)=l(6*k)], A116462 [l(k)=l(7*k)], A116463 [l(k)=l(9*k)], A117151 [l(k)=l(10*k)].

%K nonn

%O 1,1

%A _Hugo Pfoertner_, Mar 07 2006