A119491 Sum of the first n n-digit primes.

2, 24, 311, 4062, 50153, 600240, 7000409, 80000960, 900000729, 10000000754, 110000001257, 1200000001154, 13000000002051, 140000000003318, 1500000000003685, 16000000000004454, 170000000000009723, 1800000000000004696, 19000000000000007691, 200000000000000006828

Offset

1,1

Links

Alois P. Heinz, Table of n, a(n) for n = 1..300 (first 100 terms from Robert G. Wilson v)

Example

The first three three-digit primes are: 101, 103 and 107. Their sum is 311. Hence a(3) is 311.

Maple

with(numtheory): a:=n->add(ithprime(pi(nextprime(10^(n-1)))+i), i=0..n-1): seq(a(n), n=1..9); # Emeric Deutsch, Jul 29 2006

Mathematica

NextPrim[n_] := Block[{k = n + 1}, While[ !PrimeQ@k, k++ ]; k]; f[n_] := Plus @@ Rest@NestList[NextPrim, 10^(n - 1), n]; Array[f, 18] (* Robert G. Wilson v, Aug 01 2006 *)
Total/@Table[Rest[NestList[NextPrime[#]&, 10^(n-1), n]], {n, 30}] (* Harvey P. Dale, Sep 01 2022 *)

Prog

(Python)
from sympy import nextprime
def a(n):
  s = p = nextprime(10**(n-1))
  for n in range(n-1): p = nextprime(p); s += p
  return s
print([a(n) for n in range(1, 21)]) # Michael S. Branicky, Feb 24 2021

Crossrefs

Cf. A114053.

Sequence in context: A065513 A246190 A246610 * A001864 A099045 A181174

Adjacent sequences: A119488 A119489 A119490 * A119492 A119493 A119494

Keyword

base,nonn

Author

Tanya Khovanova, Jul 26 2006

Extensions

a(5)-a(8) from Emeric Deutsch, Jul 29 2006

a(9)-a(18) from Robert G. Wilson v, Aug 01 2006

Status

approved