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%I #28 Sep 08 2022 08:46:03
%S 2,5,13,28,34,36,39,111,117,123,181,184,187
%N Numbers m such that m*10^m + 1 is a semiprime.
%C This is to A007647 as semiprimes A001358 is to primes A000040. The corresponding semiprimes are A216376 = {201, 500001, 130000000000001, 280000000000000000000000000001, ...}.
%C a(14) >= 414. - _Daniel Suteu_, Jul 09 2019
%H <a href="http://factordb.com/index.php?query=414*10%5E414%2B1">Status of 414*10^414+1 in factordb.com</a>.
%e a(1) = 2 because 2 * 10^2 + 1 = 201 = 3 * 67.
%e a(2) = 5 because 5 * 10^5 + 1 = 500001 = 3 * 166667.
%e a(3) = 13 because 13*10^13 + 1 = 130000000000001 = 6529 * 19911165569.
%e a(4) = 28 because 28 * 10^28 + 1 = 29 * 9655172413793103448275862069.
%t Select[Range[40], PrimeOmega[# 10^# + 1] == 2 &] (* _Alonso del Arte_, Sep 08 2012 *)
%o (Magma) IsSemiprime:=func<i | &+[d[2]: d in Factorization(i)] eq 2>; [n: n in [1..70] | IsSemiprime(s) where s is n*10^n+1]; // _Vincenzo Librandi_, May 10 2014
%Y Cf. A001358, A007647, A064748, A216376.
%Y Cf. similar sequences listed in A242203.
%K nonn,more,hard
%O 1,1
%A _Jonathan Vos Post_, Sep 06 2012
%E a(8)-a(13) from _Daniel Suteu_, Jul 09 2019
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