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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. 1
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 (list; graph; refs; listen; history; text; internal format)
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

Cf. A001358, A213909, A213916, A275866.

Sequence in context: A106697 A323002 A249127 * A140522 A065218 A187678

Adjacent sequences:  A277333 A277334 A277335 * A277337 A277338 A277339

KEYWORD

nonn

AUTHOR

Michel Lagneau, Oct 09 2016

STATUS

approved

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Last modified February 22 10:36 EST 2020. Contains 332134 sequences. (Running on oeis4.)