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A252659
Numbers m such that 6^m - m is a semiprime.
2
2, 3, 5, 10, 15, 23, 34, 37, 47, 70, 259, 275, 278, 497, 563
OFFSET
1,1
COMMENTS
From Robert Israel, Sep 06 2016: (Start)
Even n is in this sequence iff (6^n-n)/2 is prime.
3*k is in this sequence iff (2*6^(3*k-1)-k is prime.
Also contains 275, 278 and 683.
The only other possible member less than 275 is 259. (End)
a(16) >= 617. - Kevin P. Thompson, Apr 29 2022
EXAMPLE
2 is in this sequence because 6^2-2 = 2*17 is semiprime.
10 is in this sequence because 6^10-10 = 2*30233083 and these two factors are prime.
MAPLE
Res:= NULL:
for n from 1 to 100 do
F:= ifactors(6^n-n, easy)[2];
if add(t[2], t=F) >= 3 or (hastype(F, symbol) and add(t[2], t=F) >= 2)
then flag:= false
elif add(t[2], t=F) = 2 and not hastype(F, symbol) then flag:= true
else
flag:= evalb(numtheory:-bigomega(6^n-n)=2)
fi;
if flag then Res:= Res, n fi
od:
Res; # Robert Israel, Sep 06 2016
MATHEMATICA
Select[Range[90], PrimeOmega[6^# - #]== 2&]
PROG
(Magma) IsSemiprime:=func<i | &+[d[2]: d in Factorization(i)] eq 2>; [m: m in [1..90] | IsSemiprime(s) where s is 6^m-m];
CROSSREFS
Cf. similar sequences listed in A252656.
Sequence in context: A043859 A043868 A048329 * A004691 A133335 A062925
KEYWORD
nonn,more
AUTHOR
Vincenzo Librandi, Dec 21 2014
EXTENSIONS
a(11)-a(15) from Kevin P. Thompson, Apr 29 2022
STATUS
approved