cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

Original entry on oeis.org

75, 4225, 277048, 21171189, 1709600811, 142913828920, 12272577818050, 1075207199997332, 95673602693282038, 8617752113620426557, 783964147695858014234, 71904055278788602481892, 6640510710493148698166594, 616876923984020487671442310, 57596211829372496930445843340
Offset: 1

Views

Author

Enoch Haga, Oct 14 2007

Keywords

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

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

A134230 a(n) = (10^n+1)^2-1.

Original entry on oeis.org

3, 120, 10200, 1002000, 100020000, 10000200000, 1000002000000, 100000020000000, 10000000200000000, 1000000002000000000, 100000000020000000000, 10000000000200000000000, 1000000000002000000000000, 100000000000020000000000000, 10000000000000200000000000000
Offset: 0

Views

Author

Enoch Haga, Oct 14 2007

Keywords

Comments

Previous name was: -1 + Sum of first 10^n + 1 odd numbers.

Links

Crossrefs

Cf. A134228, A134229.

Programs

  • Mathematica
    LinearRecurrence[{110,-1000},{3,120},15] (* or *) CoefficientList[Series[-3*(70*x-1) / ((10*x-1)*(100*x-1)),{x,0,14}],x] (* James C. McMahon, Apr 05 2025 *)
  • PARI
    Vec(-3*(70*x-1)/((10*x-1)*(100*x-1))  + O(x^100)) \\ Colin Barker, Jan 27 2015

Formula

a(n) = (10^n+1)^2-1. - N. J. A. Sloane, Oct 15 2007
a(n) = 110*a(n-1)-1000*a(n-2). - Colin Barker, Jan 27 2015
G.f.: -3*(70*x-1) / ((10*x-1)*(100*x-1)). - Colin Barker, Jan 27 2015

Extensions

Edited by N. J. A. Sloane, Oct 15 2007
Offset and name corrected by Arkadiusz Wesolowski, Jun 12 2013
New name (using formula by N. J. A. Sloane) from Joerg Arndt, Jan 27 2015
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Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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