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.

A077388 Row sums of the triangle in A122820.

Original entry on oeis.org

2, 8, 15, 36, 395, 72, 119, 240, 2349, 300, 539, 276, 923, 714, 435, 496, 629, 702, 2375, 1120, 1995, 1144, 874, 3192, 3925, 2938, 9531, 1960, 10063, 2670, 3441, 4448, 5907, 6358, 9835, 4464, 5069, 3610, 13533, 4000, 6273, 4410, 21113, 12012, 8325
Offset: 1

Views

Author

Amarnath Murthy, Nov 06 2002

Keywords

Comments

19318176 = A077388(1296) = A077388(2088). Are there any other pairs?. - Naohiro Nomoto, May 17 2003

Crossrefs

Cf. A054892, A077389, A082638, A122820.

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];Total /@ Table[f[n], {n, 45}] (* Ray Chandler, Oct 09 2006 *)

Extensions

More terms from Sascha Kurz, Jan 30 2003
Name corrected by Sean A. Irvine, May 18 2025

A077389 Smallest integer that is the average of n consecutive primes.

Original entry on oeis.org

2, 4, 5, 9, 79, 12, 17, 30, 261, 30, 49, 23, 71, 51, 29, 31, 37, 39, 125, 56, 95, 52, 38, 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, 110, 200, 485, 251, 155, 315
Offset: 1

Views

Author

Amarnath Murthy, Nov 06 2002

Keywords

Examples

			a(5) = 79 because the average of the 5 consecutive primes 71, 73, 79, 83, and 89 is 79, and this is the smallest such set: for example, the average of 7, 11, 13, 17, and 19 is 13.4, which is not an integer.

Links

Crossrefs

Cf. A054892, A077388, A082592, A122820.

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];Mean /@ Table[f[n], {n, 58}] (* Ray Chandler, Oct 09 2006 *)
  • PARI
    a(n) = {my(v=primes(n), s=vecsum(v), p=prime(n)); while(s%n, s-=v[1]-p=nextprime(p+1); v=concat(v[2..n], p)); s/n; } \\ Jinyuan Wang, Sep 05 2020

Formula

a(n) = A077388(n)/n.

Extensions

More terms from Sascha Kurz, Jan 30 2003
Change to definition based on comment by Zak Seidov, Mar 20 2013

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)).
Showing 1-3 of 3 results.

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