A277336 Numbers n for which the sum of the odd members and the sum of the even members in the Collatz (3x+1) trajectory are both semiprime.

6, 12, 24, 35, 61, 76, 96, 118, 146, 162, 230, 245, 338, 362, 384, 426, 444, 460, 472, 580, 584, 605, 642, 645, 664, 697, 718, 740, 790, 804, 812, 814, 830, 852, 877, 920, 926, 954, 979, 1098, 1178, 1192, 1216, 1332, 1334, 1406, 1415, 1446, 1452, 1454, 1459

Offset: 1

Author

Michel Lagneau, Oct 09 2016

Keywords

• nonn

Comments

The corresponding pairs of semiprimes are (9, 46), (9, 58), (9, 82), (94, 446), (178, 838), (95, 538), (9, 226), (411, 1894), (20499, 82366), (259, 1366), (493, 2446), (362, 1942), ...

Examples

			6 is in the sequence because the Collatz trajectory is 6 -> 3 -> 10 -> 5 -> 16 -> 8 -> 4 -> 2 -> 1 => the sum of the odd members is 3 + 5 + 1 = 9 = 3*3 and the sum of the even members is 6 + 10 + 16 + 8 + 4 + 2 = 46 = 2*23.
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001358, A213909, A213916, A275866.

Programs

Mathematica

coll[n_]:=NestWhileList[If[EvenQ[#],#/2,3#+1]&,n,#>1&];a:=Select[coll[n],OddQ[#]&];b:=Select[coll[n],EvenQ[#]&];Do[s1=Sum[a[[i]],{i,1,Length[a]}];s2=Sum[b[[j]],{j,1,Length[b]}];If[PrimeOmega[s1]==2&&PrimeOmega[s2]==2,Print[n]],{n,1,1500}]

PARI

is(n)=my(e,o=1); while(n>1, if(n%2, o+=n; n+=2*n+1, e+=n; n/=2)); isprime(e/2) && bigomega(o)==2 \\ Charles R Greathouse IV, Oct 09 2016