A227689 a(n) is the least integer k such that 2^k - 1 has at least 10^n digits.

1, 30, 329, 3319, 33216, 332190, 3321925, 33219278, 332192807, 3321928092, 33219280946, 332192809486, 3321928094885, 33219280948871, 332192809488733, 3321928094887360, 33219280948873621, 332192809488736232, 3321928094887362345, 33219280948873623476

Offset

0,2

Links

Alois P. Heinz, Table of n, a(n) for n = 0..1000

Wikipedia, Great Internet Mersenne Prime Search

Formula

a(n) = ceiling(log_2(10^(10^n-1)+1)).

Limit_{n -> oo} a(n)/10^n = log_2(10) = A020862. - Alois P. Heinz, Jun 28 2021

Example

For n = 2, A000225(328) has 99 digits and A000225(329) has 100 digits, so a(2) = 329.

Prog

(PARI) a(n) = ceil(log(10^(10^n-1)+1)/log(2)); \\ Michel Marcus, Jun 28 2021

Crossrefs

See A000225, A020862, A034887.

Sequence in context: A141216 A159543 A362521 * A006859 A341557 A107967

Adjacent sequences: A227686 A227687 A227688 * A227690 A227691 A227692

Keyword

nonn,base

Author

Olivier de Mouzon, Jul 19 2013

Extensions

a(7)-a(19) from Alois P. Heinz, Jun 28 2021

Status

approved