A276195 Smallest prime >= decimal expansion of Pi truncated to n places (A011545).

3, 31, 317, 3163, 31469, 314159, 3141601, 31415971, 314159311, 3141592661, 31415926541, 314159265359, 3141592653601, 31415926535933, 314159265359057, 3141592653589861, 31415926535897999, 314159265358979347, 3141592653589793239, 31415926535897932429, 314159265358979323861

Offset: 0

Author

Ilya Gutkovskiy, Aug 24 2016

Keywords

• nonn
• base

Examples

			a(6) = 3141601, since this is the smallest prime >= floor(Pi*10^6) = 3141592.
Pi = 3.1415926535897932384626433832795028841971…
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 0..100
• Eric Weisstein's World of Mathematics, Next Prime
• Eric Weisstein's World of Mathematics, Pi and Pi Digits
• Eric Weisstein's World of Mathematics, Pi-Prime
• Index entries for sequences related to the number Pi
• Index entries related to "constant primes"

Crossrefs

Cf. A000040, A000720, A000796, A005042, A007918, A011545, A060421.

Programs

Mathematica

Table[NextPrime[Floor[Pi 10^n] - 1], {n, 0, 20}]
Module[{nn=30,pid},pid=RealDigits[Pi,10,nn][[1]];Table[NextPrime[FromDigits[Take[pid,n]]-1],{n,nn}]] (* Harvey P. Dale, Mar 01 2024 *)

Formula

a(n) = A007918(A011545(n)).

a(n) = A000040(A000720(A011545(n)-1)+1).

a(A060421(n)-1) = A005042(n).