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 1-4 of 4 results.

A077316 Triangle read by rows: T(n,k) is the k-th prime = 1 (mod n).

Original entry on oeis.org

2, 3, 5, 7, 13, 19, 5, 13, 17, 29, 11, 31, 41, 61, 71, 7, 13, 19, 31, 37, 43, 29, 43, 71, 113, 127, 197, 211, 17, 41, 73, 89, 97, 113, 137, 193, 19, 37, 73, 109, 127, 163, 181, 199, 271, 11, 31, 41, 61, 71, 101, 131, 151, 181, 191, 23, 67, 89, 199, 331, 353
Offset: 1

Views

Author

Amarnath Murthy, Nov 04 2002

Keywords

Examples

			Triangle begins:
   2;
   3,  5;
   7, 13, 19;
   5, 13, 17, 29;
  11, 31, 41, 61, 71;
  ...

Links

Crossrefs

Cf. A034694 (first column), A077317 (main diagonal), A077318 (row sums), A077319, A093870, A193869 (row products).

Programs

  • Maple
    Tj := proc(n,k) option remember: local j,p: if(k=0)then return 0:fi: for j from procname(n,k-1)+1 do if(isprime(n*j+1))then return j: fi: od: end: A077316 := proc(n,k) return n*Tj(n,k)+1: end: seq(seq(A077316(n,k),k=1..n),n=1..15); # Nathaniel Johnston, Sep 02 2011
  • Mathematica
    Tj[n_, k_] := Tj[n, k] = Module[{j}, If[k == 0, Return[0]];
   For[j = Tj[n, k-1]+1, True, j++, If[PrimeQ[n*j+1], Return[j]]]];
T[n_, k_] := n*Tj[n, k]+1;
Table[Table[T[n, k], {k, 1, n}], {n, 1, 15}] // Flatten (* Jean-François Alcover, Aug 02 2022, after Nathaniel Johnston *)

Extensions

Edited and extended by Franklin T. Adams-Watters, Aug 29 2006

A077318 Sum of terms in n-th row of A077316.

Original entry on oeis.org

2, 8, 39, 64, 215, 150, 791, 760, 1179, 970, 3619, 1668, 6227, 3360, 5595, 6144, 13821, 5436, 24985, 10280, 17115, 14850, 35765, 18600, 42425, 26390, 43389, 34580, 92481, 24180, 115909, 57440, 79431, 61200, 115605, 55332, 197913, 106020
Offset: 1

Views

Author

Amarnath Murthy, Nov 04 2002

Keywords

Comments

By definition a(n) == 0 (mod n).
It appears that a(n) is also the smallest sum of n distinct primes of the form n*k+1. - Omar E. Pol, Sep 03 2011

Crossrefs

Cf. A034694, A077316, A077317, A077319.

Extensions

Edited, corrected and extended by Franklin T. Adams-Watters, Aug 29 2006

A093871 a(n) is the n-th prime = -1 (mod n).

Original entry on oeis.org

2, 5, 11, 19, 89, 41, 181, 127, 251, 199, 571, 227, 1013, 433, 599, 751, 2039, 593, 2089, 859, 1637, 1429, 4001, 1103, 4049, 2053, 3779, 2267, 6263, 1499, 6571, 3583, 5279, 3943, 6089, 2879, 11321, 4597, 7331, 4919, 15497, 3779, 15307, 6599, 8009, 7681
Offset: 1

Views

Author

Amarnath Murthy, Apr 20 2004

Keywords

Comments

Main diagonal of A093870.

Links

Crossrefs

Cf. A077317, A038700, A093870.

Programs

  • Maple
    f:= proc(n) local p,count;
  count:= 0;
  for p from n-1 by n do
    if isprime(p) then
       count:= count+1;
       if count = n then return p fi
    fi
  od;
end proc:
map(f, [$1..100]); # Robert Israel, Nov 08 2019

Extensions

Edited and extended by Franklin T. Adams-Watters, Aug 29 2006

A077319 Average of terms in n-th row of A077316.

Original entry on oeis.org

2, 4, 13, 16, 43, 25, 113, 95, 131, 97, 329, 139, 479, 240, 373, 384, 813, 302, 1315, 514, 815, 675, 1555, 775, 1697, 1015, 1607, 1235, 3189, 806, 3739, 1795, 2407, 1800, 3303, 1537, 5349, 2790, 3787, 2652, 6705, 1869, 7255, 3645, 4663, 3504, 8411, 3097
Offset: 1

Views

Author

Amarnath Murthy, Nov 04 2002

Keywords

Crossrefs

Cf. A034694, A077316, A077317, A077318.

Formula

a(n) = A077318(n)/n.

Extensions

Edited, corrected and extended by Franklin T. Adams-Watters, Aug 29 2006
Showing 1-4 of 4 results.

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