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.

A132811 Arithmetic mean of the n primes starting at A132809(n), summed in A132810(n).

Original entry on oeis.org

4, 5, 9, 79, 12, 17, 30, 261, 30, 49, 23, 71, 51, 29, 31, 37, 39, 125, 56, 95, 52, 173, 133, 157, 113, 353, 70, 347, 89, 111, 139, 179, 187, 281, 124, 137, 95, 347, 100, 153, 105, 491, 273, 185, 177, 377, 199, 599, 1032, 149, 274, 277, 200, 485, 251, 155, 315, 713
Offset: 2

Views

Author

Enoch Haga, Sep 01 2007

Keywords

Examples

			a(5)=79, which is the arithmetic mean 395/5 of the n=5 primes 71=A132809(n), 73, 79, 83 and 89, which add to A132810(n)=395.

Crossrefs

Cf. A132809, A132810.

Formula

a(n)=A132810(n)/n. - R. J. Mathar, Nov 27 2007

Extensions

Edited by R. J. Mathar, Nov 27 2007

A054892 Smallest prime a(n) such that the sum of n consecutive primes starting with a(n) is divisible by n.

Original entry on oeis.org

2, 3, 3, 5, 71, 5, 7, 17, 239, 13, 29, 5, 43, 23, 5, 5, 7, 7, 79, 17, 47, 11, 2, 73, 97, 53, 271, 13, 263, 23, 41, 61, 97, 101, 181, 41, 47, 13, 233, 13, 53, 13, 359, 151, 71, 61, 239, 73, 443, 859, 29, 131, 2, 61, 313, 101, 19, 151, 521, 3, 571, 31, 7, 79, 109, 97, 53
Offset: 1

Views

Author

Labos Elemer, May 23 2000

Keywords

Comments

See A132809 for another version.
In some cases (n=1,2,25,..), like a(25)=97, the sum of 25 consecutive primes starts with the 25th prime and is divided by 25: Sum=97+...+227=3925=25*157

Examples

			a(8) = 17 since the sum of the 8 consecutive primes starting with 17 is 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 = 240, which is divisible by 8.  No prime less than 17 has this property: for example, 7 + 11 + ... + 31 = 150 which is not divisible by 8.

Links

Crossrefs

Cf. A054643, A024672, A034961, A077388, A077389, A122820, A132809.

Programs

  • Mathematica
    f[n_] := Block[{k = 1, t}, While[t = Table[Prime[i], {i, k, k + n - 1}]; Mod[Plus @@ t, n] > 0, k++ ]; t]; First /@ Table[f[n], {n, 67}] (* Ray Chandler, Oct 09 2006 *)
Module[{prs=Prime[Range[250]]},Table[SelectFirst[Partition[prs,n,1],Mod[Total[#],n]==0&],{n,70}]][[;;,1]] (* Harvey P. Dale, Jul 11 2023 *)

Formula

a(n) = min{q_1 | Sum_{i=1..n} q_i = n*X}, q_i is a prime (rarely only a(n) = prime(n)).

A132810 Smallest sum of n consecutive odd primes which is a multiple of n.

Original entry on oeis.org

3, 8, 15, 36, 395, 72, 119, 240, 2349, 300, 539, 276, 923, 714, 435, 496, 629, 702, 2375, 1120, 1995, 1144, 3979, 3192, 3925, 2938, 9531, 1960, 10063, 2670, 3441, 4448, 5907, 6358, 9835, 4464, 5069, 3610, 13533, 4000, 6273, 4410, 21113, 12012, 8325, 8142
Offset: 1

Views

Author

Enoch Haga, Sep 01 2007

Keywords

Examples

			a(5)=395, associated with A132809(5)=71=prime(20) as the first of the 5 consecutive primes, is the smallest sum of 5 consecutive odd primes which is divisible by n=5.

Links

Crossrefs

Cf. A132809, A132811.

Programs

  • Mathematica
    Table[Module[{nn=n,ncop},ncop=Total/@Partition[Prime[Range[2,2500]],nn,1];SelectFirst[ ncop,Mod[#,nn]==0&]],{n,50}] (* Harvey P. Dale, Jan 17 2023 *)

Formula

Let A132809(n)=prime(i). Then a(n)= sum(j=i...i+n-1) prime(j). - R. J. Mathar, Nov 27 2007

Extensions

The example does not match the sequence. Also the offset for all of this bunch of sequences should probably be 1. - N. J. A. Sloane, Sep 13 2007
Edited by R. J. Mathar, Nov 27 2007
Showing 1-3 of 3 results.

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

Content is available under The OEIS End-User License Agreement.