A037056 a(n)-th prime is the smallest prime containing exactly n 2's.

2, 1, 48, 331, 2490, 94500, 1283805, 1402294, 12238270, 891573671, 975688072, 77612456753, 715763987889, 748327378591, 6944174236934, 580400102242316, 5209104353769836, 5710407472211223, 510579443617388387, 4806424039483242581, 45763276831811185976, 440594267900327752100

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, A037057, A034388.

Cf. A037052, A037054, A037058, A037060, A037062, A037064, A037066, A037068, A037070.

Programs

Mathematica

(* see A037057 for f *) PrimePi[ Table[ f[n, 2], {n, 1, 13}]]

Formula

a(n) = A000720(A037057(n)). - Amiram Eldar, Jul 20 2025

Extensions

a(0)=2 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