A218086 Mersenne prime exponents of prime index equal to 1 or another Mersenne prime exponent.

2, 3, 5, 17, 127

Offset: 1

Author

Raphie Frank, Oct 20 2012

Keywords

• nonn

Comments

No others < 24036584 (see A000043, Mersenne exponents).

More formally: {n in N | 0 < d(2^n - 1) < 3 and 0 < d(2^Pi(n) - 1) < 3}; d(n) the divisor count function and Pi(n) the prime counting function.

To n = 4, this sequence = |A218386(n) - A215929(n)| = |{2, 5, 19, 257, 196687} - {0, 2, 24, 240, 196560}|

Conjecture: This sequence is complete.

Examples

			Pi(2) = 1
Pi(3) = 2
Pi(5) = 3
Pi(17) = 7
Pi(127) = 31
{2, 3, 5, 17, 127} are Mersenne prime exponents.
{1, 2, 3, 7, 31} are Mersenne prime exponents at the beginning of the 20th century. (see A008578, noncomposite numbers)
		

Crossrefs

Cf. A218386, A215929