OFFSET
1,2
COMMENTS
The semiprimes of this form are: 6, 84034, 166095446411, 11729463145748964146, 13102886255950779594655873516522994057, ...
From Robert Israel, Aug 19 2014: (Start)
If k is odd, k is in the sequence iff (k*7^k-1)/2 is prime.
If k == 1 (mod 3), k is in the sequence iff (k*7^k-1)/3 is prime.
a(10) >= 506. 506*7^506 - 1 is a 431-digit composite which apparently has not been factored.
(End)
LINKS
Paul Leyland, Factorizations of n*7^n-1
MAPLE
issemiprime:= proc(n) local F, t;
F:= ifactors(n, easy)[2];
t:= add(f[2], f=F);
if t = 1 then
if type(F[1][1], integer) then return false fi
elif t = 2 then
return not hastype(F, name)
else # t > 2
return false
fi;
F:= ifactors(n)[2];
return evalb(add(f[2], f=F)=2);
end proc:
select(n -> `if`(n::odd, isprime((n*7^n-1)/2),
issemiprime(n*7^n-1)), [$1..100]); # Robert Israel, Aug 19 2014
MATHEMATICA
Select[Range[80], PrimeOmega[# 7^# - 1]==2&]
PROG
(Magma) IsSemiprime:=func<i | &+[d[2]: d in Factorization(i)] eq 2>; [n: n in [2..80] | IsSemiprime(s) where s is n*7^n-1];
(PARI) for(n=1, 100, if(bigomega(n*7^n-1)==2, print1(n, ", "))) \\ Derek Orr, Aug 20 2014
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Vincenzo Librandi, May 12 2014
EXTENSIONS
a(1) = 1 prepended and comment amended by Harvey P. Dale, Aug 12 2014
a(8) and a(9) from Robert Israel, Aug 20 2014
STATUS
approved