A037070 a(n)-th prime is the smallest prime containing exactly n 9's.

1, 8, 46, 303, 5133, 17984, 216816, 1270607, 41146179, 420243162, 2524038155, 36159205628, 343392568900, 1955010428258, 15237833654620, 260219446617109, 2621513397605657, 24619309639366177, 233874804775621799, 684559920583084690, 20920441130654929928, 200085344903558463823

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, A037071, A034388.

Cf. A037052, A037054, A037056, A037058, A037060, A037062, A037064, A037066, A037068.

Programs

Mathematica

(* see A037071 for f *) PrimePi[ Table[ f[n, 9], {n, 1, 13}]]

Formula

a(n) = A000720(A037071(n)). - Amiram Eldar, Jul 21 2025

Extensions

One more term from Vladeta Jovovic, Jan 10 2002

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 21 2025