

A218086


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


1




OFFSET

1,1


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.


LINKS

Table of n, a(n) for n=1..5.


EXAMPLE

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
Sequence in context: A089983 A072858 A276629 * A291049 A087911 A265426
Adjacent sequences: A218083 A218084 A218085 * A218087 A218088 A218089


KEYWORD

nonn


AUTHOR

Raphie Frank, Oct 20 2012


STATUS

approved



