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.

Showing 1-3 of 3 results.

A161624 Sum of all numbers from n to n-th prime.

Original entry on oeis.org

3, 5, 12, 22, 56, 76, 132, 162, 240, 390, 441, 637, 783, 855, 1023, 1311, 1634, 1738, 2107, 2366, 2491, 2929, 3233, 3729, 4453, 4826, 5005, 5400, 5589, 6006, 7663, 8150, 8925, 9169, 10580, 10846, 11737, 12663, 13287, 14271, 15290, 15610, 17433, 17775
Offset: 1

Views

Author

Juri-Stepan Gerasimov, Jun 15 2009

Keywords

Examples

			First prime is 2, so a(1) = 1+2 = 3; fifth prime is 11, so a(5) = 5+6+7+8+9+10+11 = 56.

Links

Crossrefs

Cf. A000027, A000040, A000217, A034953, A161570.

Programs

  • Magma
    [ &+[n..NthPrime(n)]: n in [1..44] ]; // Klaus Brockhaus, Jun 14 2009
  • Mathematica
    snos[n_]:=Module[{pr=Prime[n]},((pr+n)(pr-n+1))/2]; Array[snos, 50] (* Harvey P. Dale, Jun 05 2012 *)

Formula

a(n) = Sum_{k=n..prime(n)} k.
a(n) = A034953(n) - A000217(n-1). - Michel Marcus, Feb 02 2018

Extensions

Edited and extended by Klaus Brockhaus, Jun 15 2009

A161625 Sum of all numbers from 1 up to the final digit of prime(n).

Original entry on oeis.org

3, 6, 15, 28, 1, 6, 28, 45, 6, 45, 1, 28, 1, 6, 28, 6, 45, 1, 28, 1, 6, 45, 6, 45, 28, 1, 6, 28, 45, 6, 28, 1, 28, 45, 45, 1, 28, 6, 28, 6, 45, 1, 1, 6, 28, 45, 1, 6, 28, 45, 6, 45, 1, 1, 28, 6, 45, 1, 28, 1, 6, 6, 28, 1, 6, 28, 1, 28, 28, 45, 6, 45, 28, 6, 45, 6, 45, 28, 1, 45
Offset: 1

Views

Author

Juri-Stepan Gerasimov, Jun 15 2009

Keywords

Examples

			a(1)=3=1+2. a(2)=6=1+2+3. a(3)=15=1+2+3+4+5. a(4)=28=1+2+3+4+5+6+7. a(5)=1=1. a(6)=3=1+2.

Crossrefs

Cf. A000027, A000040, A161570.

Programs

Formula

a(n)= A000217(A007652(n)). - R. J. Mathar, Jun 16 2009

Extensions

Definition reworded and a 16 split in 1,6 by R. J. Mathar, Jun 16 2009

A161626 Sum of all numbers from 2*n-1 up to prime(n).

Original entry on oeis.org

3, 3, 5, 7, 30, 36, 75, 85, 140, 264, 286, 450, 561, 595, 722, 966, 1242, 1296, 1612, 1815, 1881, 2257, 2496, 2924, 3577, 3876, 3978, 4293, 4399, 4730, 6298, 6693, 7373, 7519, 8829, 8991, 9775, 10591, 11102, 11970, 12870, 13068, 14766, 14980, 15587, 15805
Offset: 1

Views

Author

Juri-Stepan Gerasimov, Jun 15 2009

Keywords

Examples

			a(1) = 1+2 = 3;
a(2) = 3;
a(3) = 5;
a(5) = 9+10+11 = 30.

Crossrefs

Cf. A000027, A000040, A161570.

Programs

Formula

a(n) = A000217(A000040(n)) - A000217(2*n-2).

Extensions

Edited and corrected by R. J. Mathar, Oct 02 2009
Inserted a zero in an A-number - R. J. Mathar, Oct 23 2009
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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