A281195 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.

2, 808, 4801, 10408, 14661, 25072, 34338, 39328, 40384, 45902, 62627, 78547, 79134, 108674, 113264, 113474, 125310, 125344, 144172, 152949, 158979, 159382, 173034, 176778, 209202, 219920, 226565, 230090, 231350, 232207, 243482, 248389, 291200, 300364, 309406

Offset

1,1

Comments

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

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, ...}

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, ...

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

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

Links

Table of n, a(n) for n=1..35.

Example

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

Mathematica

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}]

Crossrefs

Cf. A006577, A277068.

Sequence in context: A226779 A375844 A243409 * A109555 A214898 A332182

Adjacent sequences: A281192 A281193 A281194 * A281196 A281197 A281198

Keyword

nonn

Author

Michel Lagneau, Jan 17 2017

Status

approved