%I #8 Nov 11 2016 21:51:13

%S 2,6,12,3,34,49,9,72,98,18,25,28,33,39,36,7,57,406,65,11,72,86,98,114,

%T 114,129,913,153,153,171,27,172,203,33,39,270,270,295,270,290,290,305,

%U 361,57,57,386,73,78,481,481,78,72,514,20174,609,641,641,641,641

%N Least k such that A006577(k) = A006577(n) + A006577(n+1).

%C A006577(n) is the number of halving and tripling steps to reach 1 in the '3x+1' problem.

%C The distinct squares in the sequence are 9, 25, 36, 49, 169, 361, ...

%C The distinct primes in the sequence are 2, 3, 7, 11, 31, 41, 47, 71, 73, 97, 103, ...

%H Michel Lagneau, <a href="/A277962/b277962.txt">Table of n, a(n) for n = 1..10000</a>

%H <a href="/index/3#3x1">Index entries for sequences related to 3x+1 (or Collatz) problem</a>

%e a(5)=34 because A006577(34) = 13 = A006577(5) + A006577(6) = 5 + 8.

%p nn:=3*10^6:U:=array(1..nn):V:=array(1..nn):

%p for i from 1 to nn do:

%p m:=i:it0:=0:

%p for j from 1 to nn while(m<>1) do:

%p if irem(m, 2)=0

%p then

%p m:=m/2:it0:=it0+1:

%p else

%p m:=3*m+1:it0:=it0+1:

%p fi:

%p od:

%p U[i]:=it0:

%p od:

%p for n from 1 to 60 do:

%p ii:=0:

%p for k from 1 to nn while(ii=0) do:

%p if U[k]=U[n]+ U[n+1]

%p then

%p ii:=1:printf(`%d, `, k):

%p else

%p fi:

%p od:

%p od:

%t f:=Table[Length[NestWhileList[If[EvenQ[#],#/2,3#+1]&,n,#!=1&]]-1,{n,3*10^6}];Do[k=1;While[f[[k]]!=f[[m]]+f[[m+1]],k++];Print[m," ",k],{m,1,60}]

%Y Cf. A006577.

%K nonn

%O 1,1

%A _Michel Lagneau_, Nov 06 2016