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%I #24 Sep 05 2024 10:16:16
%S 1,3,17,31,7101,14183
%N Numbers k such that 81*10^(2*k) + 9*10^k + 1 is prime.
%e 91 = 7 * 13.
%e 8191 is prime ==> a(1) = 0.
%e 810901 = 7^2 * 13 * 19 * 67.
%e 81009001 is prime ==> a(2) = 3.
%e 8100090001 = 73 * 271 * 331 * 1237.
%e 810000900001 = 1471 * 550646431.
%e 81000009000001 = 7 * 13 * 613 * 757 * 1129 * 1699.
%e 8100000090000001 = 31 * 439 * 595194363289.
%e 810000000900000001 = 7 * 13 * 157 * 193 * 4243 * 4969 * 13933.
%e 81000000009000000001 = 271 * 298892988963099631.
%o (PARI) for(k=0, 1e3, if(ispseudoprime(81*100^k+9*10^k+1), print1(k", ")))
%Y Cf. A309738, A309743.
%K nonn,more,base,changed
%O 1,2
%A _Seiichi Manyama_, Aug 15 2019
%E a(6) from _Michael S. Branicky_, Sep 05 2024
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