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Primes of the form b*10^(2*k) + b*10^k + 1 for 1 <= b <= 9, k >= 0.
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%I #22 Aug 15 2019 07:28:59

%S 3,5,7,11,13,17,19,331,661,881,991,20201,60601,90901,2002001,5005001,

%T 300030001,600060001,50000500001,2000002000001,8000008000001,

%U 9000009000001,3000000003000000001,200000000020000000001,80000000000800000000001

%N Primes of the form b*10^(2*k) + b*10^k + 1 for 1 <= b <= 9, k >= 0.

%e b | Primes of the form b*10^(2*k) + b*10^k + 1

%e --+-------------------------------------------------------------

%e 1 | 3.

%e 2 | 5, 20201, 2002001, 2000002000001, 200000000020000000001, ...

%e 3 | 7, 331, 300030001, 3000000003000000001.

%e 4 |

%e 5 | 11, 5005001, 50000500001, ...

%e 6 | 13, 661, 60601, 600060001, ...

%e 7 |

%e 8 | 17, 881, 8000008000001, 80000000000800000000001, ...

%e 9 | 19, 991, 90901, 9000009000001, 9000000000009000000000001, ...

%Y Numbers k such that b*10^(2*k) + b*10^k + 1 are prime: A296444 (b=2), A309740 (b=5), A309741 (b=6), A309742 (b=8), A309743 (b=9).

%Y Primes of the form b*10^(2*k) + b*10^k + 1: A160432 (b=3).

%Y Cf. A309738.

%K nonn,base

%O 1,1

%A _Seiichi Manyama_, Aug 15 2019