A394308 a(n) is the number of n-digit numbers that are primes or squares of primes.

6, 23, 150, 1075, 8403, 69009, 586359, 5097659, 45088251, 404211168, 3663020003, 33489908410, 308457773970, 2858876650895, 26639629959245, 249393774420754, 2344318827941519, 22116397163851495, 209317713089633145, 1986761935587749812, 18906449884369960388, 180340017206048029364

Offset

1,1

Links

Table of n, a(n) for n=1..22.

Formula

a(n) = pi(10^n) - pi(10^(n-1)) + pi(10^(n/2)) - pi(10^((n-1)/2)).

a(n) = A006879(n) + A379566(n).

Limit_{n->oo} a(n)/a(n-1) = 10.

Mathematica

a[n_]:=PrimePi[10^n]-PrimePi[10^(n-1)]+PrimePi[10^(n/2)]-PrimePi[10^((n-1)/2)]; Array[a, 22]

Crossrefs

Cf. A000430, A000720, A001248, A006879, A122121, A379566.

Sequence in context: A219168 A013260 A013266 * A154420 A255305 A339628

Adjacent sequences: A394305 A394306 A394307 * A394309 A394310 A394311

Keyword

nonn,base

Author

Stefano Spezia, Mar 15 2026

Status

approved