A227683 Number of digits in n-th Mersenne number.

1, 1, 2, 3, 4, 4, 6, 6, 7, 9, 10, 12, 13, 13, 15, 16, 18, 19, 21, 22, 22, 24, 25, 27, 30, 31, 32, 33, 33, 35, 39, 40, 42, 42, 45, 46, 48, 50, 51, 53, 54, 55, 58, 59, 60, 60, 64, 68, 69, 69, 71, 72, 73, 76, 78, 80, 81, 82, 84, 85, 86, 89, 93, 94, 95, 96, 100

Offset: 1

Author

Olivier de Mouzon, Jul 19 2013

Keywords

• nonn
• base

Examples

			For n = 5, the fifth prime number is 11, so 2^11 - 1 = 2047 is the fifth Mersenne number, which has 4 digits, so a(5) = 4.
		

Crossrefs

Cf. A000040, A001348.

Programs

PARI

a227683(n) = floor(log(2^prime(n)-1)/log(10)) + 1 \\ Michael B. Porter, Jul 20 2013

Formula

a(n) = floor(log_10(A001348(n))) + 1.