OFFSET
1,1
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), ...
LINKS
Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
EXAMPLE
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.
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}]
PROG
(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
CROSSREFS
KEYWORD
nonn
AUTHOR
Michel Lagneau, Oct 09 2016
STATUS
approved