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

1,3

Links

Table of n, a(n) for n=1..67.

Formula

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

Example

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.

Prog

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

Crossrefs

Cf. A000040, A001348.

Sequence in context: A063208 A343912 A262265 * A321166 A092988 A304575

Adjacent sequences: A227680 A227681 A227682 * A227684 A227685 A227686

Keyword

nonn,base

Author

Olivier de Mouzon, Jul 19 2013

Status

approved