A134228 Sum of the odd primes <= 2*10^n.

75, 4225, 277048, 21171189, 1709600811, 142913828920, 12272577818050, 1075207199997332, 95673602693282038, 8617752113620426557, 783964147695858014234, 71904055278788602481892, 6640510710493148698166594, 616876923984020487671442310, 57596211829372496930445843340

Offset: 1

Author

Enoch Haga, Oct 14 2007

Keywords

• nonn

Examples

			a(1) = 75 because that is the sum of odds (3+5+7+11+13+17+19=75) less composites (9,15,21) under 10^1 (beginning with 3).
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..19 (calculated using Kim Walisch's primesum program)
• Kim Walisch, Sum of the primes below x (primesum).

Crossrefs

Cf. A007504, A007917, A049084, A134229, A134230.

Programs

PARI

list(nmax) = {my(s = 0, m = 20, n = 1); forprime(p = 3, , if(p > m, print1(s, ", "); if(n == nmax, break); n++; m *= 10); s += p);} \\ Amiram Eldar, Jan 18 2025

PARI

a(n) = vecsum(primes([3,2*10^n])); \\ Michel Marcus, Jan 18 2025

Formula

Beginning with 3, compute 10^n sums of odds, less odd composites, for each 10^n.

From R. J. Mathar, Oct 28 2007: (Start)

a(n) = Sum_{p: p in A000040} (2 < p <= 2*10^n).

a(n) = A007504(k)-2, where k = A049084(A007917(2*10^n)). (End)

Extensions

Better definition from R. J. Mathar, Oct 28 2007

a(9)-a(14) from Hiroaki Yamanouchi, Jul 06 2014

a(15) from Amiram Eldar, Jan 18 2025