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).
A030481
Squares of primes, with property that all even digits occur together and all odd digits occur together.
Original entry on oeis.org
4, 9, 25, 49, 289, 841, 2209, 2809, 4489, 6241, 6889, 22201, 22801, 24649, 66049, 80089, 208849, 426409, 466489, 822649, 2042041, 2468041, 2866249, 2886601, 4068289, 6046681, 6086089, 6466849, 6806881, 6848689, 8082649, 8288641, 8462281, 8826841, 22648081, 26020201, 26822041, 28440889, 44262409
Offset: 1
Includes (2*10^(2k) + 2*10^k + 1)^2 for k in
A296444.
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filter:= proc(n) local L;
convert(convert(floor(n/10),base,10),set) mod 2 = {0}
end proc:
[4, 9, op(select(filter, [seq(ithprime(i)^2, i=3..20000)]))]; # Robert Israel, Jan 04 2024
A296443
Numbers k such that 2*10^(2k)-2*10^k+1 is prime.
Original entry on oeis.org
1, 2, 6, 7, 8, 315, 667, 5125, 7301, 10500, 11096
Offset: 1
181, 19801, 1999998000001, 199999980000001, and 19999999800000001 are prime, while 1998001=277*7213, 199980001=13*41*457*821, and 19999800001=53*5953*63389.
See
A296444 for 2*10^(2k)+2*10^k+1.
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ParallelMap[If[PrimeQ[2*10^(2 #) - 2*10^# + 1], #, Nothing] &, Range@ 4000] (* Robert G. Wilson v, Dec 13 2017 *)
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isok(k) = isprime(2*10^(2*k)-2*10^k+1); \\ Michel Marcus, Dec 13 2017
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