A037058 a(n)-th prime is the smallest prime containing exactly n 3's.

1, 2, 51, 345, 2602, 27062, 232466, 1935248, 17950160, 155123231, 1022275037, 13076476440, 119921146473, 1100928006234, 9986615648246, 39453679683959, 636484070277727, 8477216022186037, 80079195779613271, 758351887226957873, 7209429409009441899, 68676498683402943115

Offset: 0

Author

Patrick De Geest, Jan 04 1999

Keywords

• nonn
• base
• hard

Links

• Andrew R. Booker, The Nth Prime Page.
• Kim Walisch, primecount, Fast prime counting function library.

Crossrefs

Cf. A000720, A037059, A034388.

Cf. A037052, A037054, A037056, A037060, A037062, A037064, A037066, A037068, A037070.

Programs

Mathematica

(* see A037059 for f *) PrimePi[ Table[ f[n, 3], {n, 1, 13}]]

Formula

a(n) = A000720(A037059(n)). - Amiram Eldar, Jul 20 2025

Extensions

Edited and extended by Robert G. Wilson v, Jul 04 2003

a(0)=1 prepended by Sean A. Irvine, Dec 06 2020

a(14)-a(21) calculated using Kim Walisch's primecount and added by Amiram Eldar, Jul 20 2025