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A252659
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Numbers m such that 6^m - m is a semiprime.
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2
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2, 3, 5, 10, 15, 23, 34, 37, 47, 70, 259, 275, 278, 497, 563
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OFFSET
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1,1
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COMMENTS
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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)
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LINKS
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EXAMPLE
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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.
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MAPLE
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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:
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MATHEMATICA
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Select[Range[90], PrimeOmega[6^# - #]== 2&]
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PROG
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(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];
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CROSSREFS
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Cf. similar sequences listed in A252656.
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KEYWORD
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nonn,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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