A309739
Primes of the form b*10^(2*k) + b*10^k + 1 for 1 <= b <= 9, k >= 0.
Original entry on oeis.org
3, 5, 7, 11, 13, 17, 19, 331, 661, 881, 991, 20201, 60601, 90901, 2002001, 5005001, 300030001, 600060001, 50000500001, 2000002000001, 8000008000001, 9000009000001, 3000000003000000001, 200000000020000000001, 80000000000800000000001
Offset: 1
b | Primes of the form b*10^(2*k) + b*10^k + 1
--+-------------------------------------------------------------
1 | 3.
2 | 5, 20201, 2002001, 2000002000001, 200000000020000000001, ...
3 | 7, 331, 300030001, 3000000003000000001.
4 |
5 | 11, 5005001, 50000500001, ...
6 | 13, 661, 60601, 600060001, ...
7 |
8 | 17, 881, 8000008000001, 80000000000800000000001, ...
9 | 19, 991, 90901, 9000009000001, 9000000000009000000000001, ...
Primes of the form b*10^(2*k) + b*10^k + 1:
A160432 (b=3).
A306751
Numbers k such that 9*10^(2*k) + 3*10^k + 1 is prime.
Original entry on oeis.org
0, 5, 14, 77, 104, 2603, 2657, 24029
Offset: 1
13 is prime ==> a(1) = 0.
931 = 7^2 * 19.
90301 = 73 * 1237.
9003001 = 7 * 757 * 1699.
900030001 = 13 * 4969 * 13933.
90000300001 is prime ==> a(2) = 5.
-
for(k=0, 1e3, if(ispseudoprime(9*100^k+3*10^k+1), print1(k", ")))
A309744
Numbers k such that 81*10^(2*k) + 9*10^k + 1 is prime.
Original entry on oeis.org
1, 3, 17, 31, 7101, 14183
Offset: 1
91 = 7 * 13.
8191 is prime ==> a(1) = 0.
810901 = 7^2 * 13 * 19 * 67.
81009001 is prime ==> a(2) = 3.
8100090001 = 73 * 271 * 331 * 1237.
810000900001 = 1471 * 550646431.
81000009000001 = 7 * 13 * 613 * 757 * 1129 * 1699.
8100000090000001 = 31 * 439 * 595194363289.
810000000900000001 = 7 * 13 * 157 * 193 * 4243 * 4969 * 13933.
81000000009000000001 = 271 * 298892988963099631.
-
for(k=0, 1e3, if(ispseudoprime(81*100^k+9*10^k+1), print1(k", ")))
Showing 1-3 of 3 results.