A282974 Numbers k such that A011546(k-1) is a prime.

1, 2, 6, 12, 1902, 3971, 5827, 16208, 47577

Offset: 1

Author

XU Pingya, Feb 25 2017

Keywords

• nonn
• base
• more
• hard

Comments

Round(k)=floor(k) or floor(k)+1, so if round(k)=floor(k) and floor(k) is a prime number, then round(k) is also prime. Thus 47577 = A060421(6) and 613373 = A060421(8) are also terms.

The corresponding primes are in A282973.

a(10) > 2^16. - Lucas A. Brown, Apr 05 2021

Links

• Lucas A. Brown, A282974.py
• Eric Weisstein's World of Mathematics, Pi-Prime

Crossrefs

Cf. A000796, A005042, A011546, A060421, A282973.

Programs

Mathematica

Do[If[PrimeQ[Round[Pi*10^(n-1)]],Print[n]],{n,17511}]

PARI

default(realprecision, 10^5); x=Pi;
is(k) = ispseudoprime(round(x*10^k--)); \\ Jinyuan Wang, Mar 27 2020

Extensions

a(8) and a(9) from Lucas A. Brown, Apr 05 2021

Definition corrected by Lucas A. Brown, Apr 05 2021