A281195 - OEIS

%I #6 Jan 19 2017 04:52:38

%S 2,808,4801,10408,14661,25072,34338,39328,40384,45902,62627,78547,

%T 79134,108674,113264,113474,125310,125344,144172,152949,158979,159382,

%U 173034,176778,209202,219920,226565,230090,231350,232207,243482,248389,291200,300364,309406

%N Numbers m such that gcd(s1,s2) = number of the Collatz iterations of m where s1 is the sum of the odd terms and s2 the sum of the even terms in the Collatz trajectory.

%C Or numbers m such that A277068(m) = A006577(m).

%C The corresponding values of gcd(s1,s2) are given by the sequence {b(n)} = {1, 28, 121, 29, 45, 64, 80, 44, 44, 70, 86, 138, 76, 40, 105, 105, 180, 56, 43, 82, 170, 46, 72, 72, 111, 36, 62, 36, 137, 62, 36, 62, 26, 88, 78, 78, ...}

%C We observe pairs (b(n), b(n)) with b(n): 44, 105, 72, 78, 68, 146, 35, 74, 61, 74, 87, 77, 90, 38, 44, ...

%C We observe triples (b(n), b(n), b(n)) with b(n): 78, 35, 77, 80, 106, ...

%C We observe quadruples (b(n), b(n), b(n), b(n)) with b(n): 35, 70, ...

%e 808 is in the sequence because the Collatz trajectory is given by the 28 terms of the set {808 404 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1}. The sum of the even terms is 2408, the sum of the odd terms is 196 and gcd(2408,196) = 28.

%e Or A277068(808) = A006577(808) = 28.

%t g[n_]:=Module[{a=n,k=0},While[a!=1,k++;If[EvenQ[a],a=a/2,a=a*3+1]];k];Array[g,10^4];Collatz[n_]:=NestWhileList[If[OddQ[#],3#+1,#/2]&,n,#>1&];f[n_]:=Block[{c=Collatz@n},GCD[Plus@@Select[c,OddQ],Plus@@Select[c,EvenQ]]];Array[f,10^4];Do[If[g[m]==f[m],Print[m]],{m,1,3*10^5}]

%Y Cf. A006577, A277068.

%K nonn

%O 1,1

%A _Michel Lagneau_, Jan 17 2017