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Numbers n such that n*5^n+1 is semiprime.
1

%I #17 Sep 08 2022 08:46:08

%S 1,2,4,16,21,40,76,113,153,288

%N Numbers n such that n*5^n+1 is semiprime.

%C The semiprimes of this form are 6, 51, 2501, 2441406250001, 10013580322265626, 363797880709171295166015625001, ...

%C a(11) >= 1006. - _Hugo Pfoertner_, Aug 05 2019

%H factordb.com, <a href="http://factordb.com/index.php?query=5%5E1006*1006%2B1">Status of 1006*5^1006+1</a>.

%t Select[Range[90], PrimeOmega[# 5^# + 1] == 2 &]

%o (Magma) IsSemiprime:=func<i | &+[d[2]: d in Factorization(i)] eq 2>; [n: n in [1..90] | IsSemiprime(s) where s is n*5^n+1];

%Y Cf. similar sequences listed in A242203.

%Y Cf. A050916.

%K nonn,more,hard

%O 1,2

%A _Vincenzo Librandi_, May 10 2014

%E a(8)-a(10) from _Luke March_, Aug 13 2015