A238751 Lesser prime of third Mersenne prime pair {2^m - 5, 5*2^m - 1}.

11, 251, 1019, 4091, 65531, 4294967291

Offset: 1

Author

Ilya Lopatin and Juri-Stepan Gerasimov, Mar 04 2014

Keywords

• nonn
• more

Comments

By comparing A059608 and A001770, the next term, if it exists, is larger than 2^350028. - Giovanni Resta, Mar 06 2014

Lesser prime of Mersenne prime pair of order k and of the form {2^m - (2k - 1), (2k - 1)*2^m - 1}:

for order k = 1: 3, 7, 31, 127, 8191, 131071, ... (Mersenne primes A000668)

for order k = 2: 5, 13, 61, ...

for order k = 3: 11, 251, 1019, 4091, 655531, 4294967291, ... (this sequence)

for order k = 4:

for order k = 5: 2097143, ...

for order k = 6: 3, ...

for order k = 7:

for order k = 8: 17, 1009, 16369, ...

for order k = 9: 47, 65519, 1048559, 68719476719, ...

for order k = 10: 13, 2097133, ...

for order k = 11: 107, 8171, ...

for order k = 12: 41, 233, 4073, ...

for order k = 13: 487, ...

for order k = 14: 5, 229, 997, ...

for order k = 15: 97, ...

Examples

			11 is in this sequence because Mersenne prime pair {2^4-(2*3-1) = 11, (2*3-1)*2^4-1 = 79} where 3 is order and 11 is lesser prime (for m = 4).
		

Crossrefs

Cf. A237422, A238694, A238749, A059608, A001770, A156560, A050522.

Programs

Mathematica

2^Select[Range[1000], PrimeQ[2^# - 5] && PrimeQ[5*2^# - 1] &] - 5 (* Giovanni Resta, Mar 06 2014 *)

Formula

Numbers 2^m - 5 for m belonging to the intersection of A001770 and A059608. - Max Alekseyev, Feb 20 2024