A277064 Decimal expansion of (sqrt(3)-1)^(sqrt(2)-1).

8, 7, 8, 8, 0, 2, 2, 0, 4, 8, 5, 5, 4, 4, 0, 6, 4, 8, 2, 5, 4, 2, 4, 5, 0, 2, 4, 5, 6, 5, 0, 6, 6, 5, 2, 2, 4, 1, 5, 8, 9, 5, 1, 5, 9, 1, 8, 6, 3, 1, 8, 0, 6, 4, 9, 3, 1, 3, 7, 3, 4, 1, 5, 2, 8, 8, 8, 0, 5, 3, 8, 3, 0, 0, 7, 8, 7, 2, 3, 8, 7, 6, 3, 4, 7, 7, 0, 4, 0, 7, 3, 7, 6, 0, 7, 3, 0, 9, 6, 8, 2, 1, 4, 4, 7

Offset

0,1

Comments

It is easy to see that there are no primes with more than one digit in the first 37 decimal places of (sqrt(3)-1)^(sqrt(2)-1). All primes with more than one digit end in 1, 3, 7, or 9. The only 1, 3, 7, or 9 in the first 37 decimal places of (sqrt(3)-1)^(sqrt(2)-1) is the 7 that is two digits after the decimal point. Since 87 = 3*29, there are no primes with more than one digit in the first 37 decimal places of (sqrt(3)-1)^(sqrt(2)-1). There are multidigit primes ending at the 38th decimal place, such as 41, 241, and 652241.

Links

G. C. Greubel, Table of n, a(n) for n = 0..10000

Bobby Jacobs, Prime Curios

Example

0.8788022048554406482542450245650665224...

Maple

evalf((sqrt(3)-1)^(sqrt(2)-1), 110); # Muniru A Asiru, Oct 11 2018

Mathematica

First@ RealDigits[N[(Sqrt[3] - 1)^(Sqrt[2] - 1), 120]] (* Michael De Vlieger, Sep 27 2016 *)

Prog

(PARI) (sqrt(3)-1)^(sqrt(2)-1) \\ Rick L. Shepherd, Nov 23 2016
(Magma) SetDefaultRealField(RealField(100)); (Sqrt(3)-1)^(Sqrt(2)-1); // G. C. Greubel, Oct 10 2018

Crossrefs

Sequence in context: A203914 A037077 A094106 * A276762 A363874 A256609

Adjacent sequences: A277061 A277062 A277063 * A277065 A277066 A277067

Keyword

nonn,cons

Author

Bobby Jacobs, Sep 27 2016

Extensions

Extended and offset corrected by Rick L. Shepherd, Nov 23 2016

Status

approved