A120357 a(n) is the smallest prime p such that 2^p-1 (a Mersenne number) contains 10^n or more decimal digits.

2, 31, 331, 3319, 33223, 332191, 3321937, 33219281, 332192831, 3321928097, 33219280951, 332192809589, 3321928094941, 33219280948907, 332192809488739, 3321928094887411, 33219280948873687, 332192809488736253

Offset: 0

Author

G. L. Honaker, Jr., Jun 25 2006

Keywords

• base
• nonn

Comments

For n>0 almost all digits of a(n) from the left are equal to the first terms of the expansion Log[10]/Log[2] = {3, 3, 2, 1, 9, 2, 8, 0, 9, 4, 8, 8, 7, 3, 6, 2, 3, 4, 7, 8, 7, 0, 3, 1, 9, 4, 2, 9, 4, 8, 9, 3, 9, ...} = A020862(n). - Alexander Adamchuk, Jan 16 2007

Examples

			E.g. a(7)=33219281 because 2^33219281-1 is the smallest Mersenne number that contains 10^7 (ten million) or more decimal digits.
		

Links

• Farideh Firoozbakht, Table of n, a(n) for n = 0..29
• G. L. Honaker, Jr. and Chris Caldwell, Prime Curios! 33219281
• Author?, GIMPS [Broken link?]

Crossrefs

Cf. A001348.

Cf. A020862 = decimal expansion of log(10)/log(2).

Extensions

More terms from Farideh Firoozbakht, Jul 22 2006