A228027
Primes of the form 4^k + 9.
Original entry on oeis.org
13, 73, 1033, 262153, 1073741833, 73786976294838206473, 4835703278458516698824713
Offset: 1
262153 is a term because 4^9 + 9 = 262153 is prime.
Cf. Primes of the form r^k + h:
A092506 (r=2, h=1),
A057733 (r=2, h=3),
A123250 (r=2, h=5),
A104066 (r=2, h=7),
A104070 (r=2, h=9),
A057735 (r=3, h=2),
A102903 (r=3, h=4),
A102870 (r=3, h=8),
A102907 (r=3, h=10),
A290200 (r=4, h=1),
A228026 (r=4, h=3), this sequence (r=4, h=9),
A182330 (r=5, h=2),
A228029 (r=5, h=6),
A102910 (r=5, h=8),
A182331 (r=6, h=1),
A104118 (r=6, h=5),
A104115 (r=6, h=7),
A104065 (r=7, h=4),
A228030 (r=7, h=6),
A228031 (r=7, h=10),
A228032 (r=8, h=3),
A228033 (r=8, h=5),
A144360 (r=8, h=7),
A145440 (r=8, h=9),
A228034 (r=9, h=2),
A159352 (r=10, h=3),
A159031 (r=10, h=7).
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[a: n in [0..200] | IsPrime(a) where a is 4^n+9];
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Select[Table[4^n + 9, {n, 0, 200}],PrimeQ]
A228033
Primes of the form 8^k + 5.
Original entry on oeis.org
13, 2787593149816327892691964784081045188247557, 15177100720513508366558296147058741458143803430094840009779784451085189728165691397
Offset: 1
Cf. Primes of the form k^n + h:
A092506 (k=2, h=1),
A057733 (k=2, h=3),
A123250 (k=2, h=5),
A104066 (k=2, h=7),
A104070 (k=2, h=9),
A057735 (k=3, h=2),
A102903 (k=3, h=4),
A102870 (k=3, h=8),
A102907 (k=3, h=10),
A290200 (k=4, h=1),
A182330 (k=5, h=2),
A102910 (k=5, h=8),
A182331 (k=6, h=1),
A104118 (k=6, h=5),
A104115 (k=6, h=7),
A104065 (k=7, h=4), this sequence (k=8, h=5),
A144360 (k=8, h=7),
A145440 (k=8, h=9),
A228034 (k=9, h=2),
A159352 (k=10, h=3),
A159031 (k=10, h=7).
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[a: n in [1..300] | IsPrime(a) where a is 8^n+5];
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Select[Table[8^n + 5, {n, 4000}], PrimeQ]
A228028
Primes of the form 5^n + 4.
Original entry on oeis.org
5, 29, 15629, 9765629
Offset: 1
Cf. Primes of the form k^n + h:
A092506 (k=2, h=1),
A057733 (k=2, h=3),
A123250 (k=2, h=5),
A104066 (k=2, h=7),
A104070 (k=2, h=9),
A057735 (k=3, h=2),
A102903 (k=3, h=4),
A102870 (k=3, h=8),
A102907 (k=3, h=10),
A290200 (k=4, h=1),
A228027 (k=4, h=9),
A182330 (k=5, h=2), this sequence (k=5, h=4),
A228029 (k=5, h=6),
A102910 (k=5, h=8),
A182331 (k=6, h=1),
A104118 (k=6, h=5),
A104115 (k=6, h=7),
A104065 (k=7, h=4),
A228030 (k=7, h=6),
A228031 (k=7, h=10),
A228032 (k=8, h=3),
A228033 (k=8, h=5),
A144360 (k=8, h=7),
A145440 (k=8, h=9),
A228034 (k=9, h=2),
A159352 (k=10, h=3),
A159031 (k=10, h=7).
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[a: n in [0..200] | IsPrime(a) where a is 5^n+4];
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Select[Table[5^n + 4, {n, 0, 200}], PrimeQ]
A356987
Primes whose decimal expansion is 1, zero or more 0's, then a single digit.
Original entry on oeis.org
11, 13, 17, 19, 101, 103, 107, 109, 1009, 10007, 10009, 100003, 1000003, 100000007, 1000000007, 1000000009, 100000000003, 100000000000000003, 1000000000000000003, 1000000000000000009, 10000000000000000000009, 1000000000000000000000007
Offset: 1
1000000007 is a term because it is a prime number whose decimal expansion is 1, 8 zeros, then the single digit 7.
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PrmsUpTo10PowNpl9[n_] := Parallelize @ Cases[ Table[10^k+m,{k,n},{m,{1,3,7,9}}], ?PrimeQ, {2}]; PrmsUpTo10PowNpl9[1000] (* _Mikk Heidemaa, Jan 07 2023 *)
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from itertools import count, islice
from sympy import isprime
def A356987_gen(): # generator of terms
return filter(isprime,(10**k+m for k in count(1) for m in (1,3,7,9)))
A356987_list = print(list(islice(A356987_gen(),30))) # Chai Wah Wu, Oct 22 2022
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