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%I #12 Jan 23 2022 20:03:47
%S 1,5,44,56,187,192,206,16561
%N Numbers k such that k * 10^k * (10^k - 1)/9 + 1 is prime.
%C There are no more terms up to k = 4000 (cf. link).
%C There are no more terms up to k = 14600. - _Jason Earls_, Nov 30 2009
%D J. Earls, Mathematical Bliss, Pleroma Publications, 2009, page 55. ASIN: B002ACVZ6O [From _Jason Earls_, Nov 22 2009]
%H Jason Earls, <a href="http://www.helium.com/items/106012-biography-enrico-bombieri-fields-medal-winner?page=2">Biography: Enrico Bombieri, Fields Medal winner</a>
%e For k=5, k * 10^k * (10^k - 1)/9 + 1 is the prime 5555500001, so 5 is a term.
%o (Magma) [ x[1]: x in [ < n, Integers()!(n*10^n*(10^n - 1)/9 + 1) >: n in [1..186] ] | IsPrime(x[2]) ];
%o (PARI) is(n)=ispseudoprime(n*10^n*(10^n-1)/9+1) \\ _Charles R Greathouse IV_, Jun 13 2017
%Y Cf. A002275 (repunits: (10^n - 1)/9).
%K nonn,more
%O 1,2
%A _Lekraj Beedassy_, Apr 09 2009
%E Edited by _Klaus Brockhaus_, Apr 11 2009
%E a(8) from Herman Jamke (hermanjamke(AT)fastmail.fm), Oct 03 2010