A117881 First semiprime after Pi^n.

4, 4, 10, 33, 106, 309, 965, 3022, 9489, 29813, 93649, 294209, 924271, 2903678, 9122173, 28658147, 90032221, 282844574, 888582413, 2791563955, 8769956797, 27551631845, 86556004193, 271923706897, 854273519921, 2683779414319

Offset: 0

Author

Jonathan Vos Post, May 02 2006

Keywords

• easy
• nonn

Comments

Pi and semiprime analog of A074496 First prime after e^n. Lim_{n->infinity} a(n+1)/a(n) = Pi. See also A000796 Decimal expansion of Pi. There are numbers where floor(Pi^n) is itself a semiprime, as with floor(Pi^2) = 9, floor(Pi^6) = 961 = 31^2, floor(Pi^9) = 29809 = 13 * 2293, floor(Pi^25) = 2683779414317 = 5749 * 466825433.

Examples

			a(3) = 33 because Pi^3 = 31.0062766... floor(Pi^3) = 31 is prime hence 31 + 2 = 33 is a term.
		

Links

• Eric Weisstein's World of Mathematics, e-Prime.

Crossrefs

Cf. A000040, A000149, A000796, A001358, A007512, A014210, A050808, A050809, A059303, A064118, A095935, A115019, A074496, A118840.

Programs

Mathematica

fsp[n_]:=Module[{k=Ceiling[Pi^n]},While[PrimeOmega[k]!=2,k++];k]; Array[fsp,30,0]

Formula

a(n) = min{s in A001358 and s > Pi^n}.