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 1-5 of 5 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

A077317 a(n) is the n-th prime == 1 (mod n).

Original entry on oeis.org

2, 5, 19, 29, 71, 43, 211, 193, 271, 191, 661, 277, 937, 463, 691, 769, 1531, 613, 2357, 1021, 1723, 1409, 3313, 1609, 3701, 2029, 3187, 2437, 6961, 1741, 7193, 3617, 4951, 3877, 7001, 3169, 10657, 6271, 7879, 5521, 13613, 3823, 15137, 7349, 9091, 7499
Offset: 1

Views

Author

Amarnath Murthy, Nov 04 2002, Jul 23 2005 (submitted incorrectly on two separate occasions; each time it has had to be corrected)

Keywords

Comments

a(n) is the n-th prime in the arithmetic progression with first term 1 and common difference n.
Main diagonal of A077316.

Examples

			a(5) = 71, the fifth prime in the sequence 1, 6, 11, 16, 21, 26, 31, 36, 41, 46, 51, 56, 61, 66, 71, ...

Links

Crossrefs

Cf. A034694, A077316, A077318, A077319, A093871.

Programs

  • Maple
    a:=proc(n) local N, B, j: N:=[seq(n*x+1,x=0..500)]: B:={}: for j from 1 to nops(N) do if isprime(N[j])=true then B:=B union {N[j]} else fi od: B[n]: end: seq(a(n),n=1..55); # Emeric Deutsch, Sep 03 2005
  • Mathematica
    Module[{nn=50,prs=Prime[Range[3000]]},Join[{2},Table[Select[prs,Mod[#,n] == 1&][[n]],{n,2,nn}]]] (* Harvey P. Dale, Nov 13 2020 *)

Extensions

Edited, corrected and extended by Emeric Deutsch, Sep 03 2005 and by Franklin T. Adams-Watters, Aug 29 2006
Edited by N. J. A. Sloane, Aug 23 2008 at the suggestion of R. J. Mathar

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

A194267 Smallest sum of three distinct primes of the form n*k+1.

Original entry on oeis.org

10, 15, 39, 35, 83, 39, 143, 131, 129, 83, 179, 111, 263, 143, 243, 227, 479, 129, 839, 203, 381, 179, 463, 363, 503, 263, 543, 339, 641, 243, 1367, 547, 597, 479, 563, 219, 965, 839, 549, 563, 1643, 381, 1551, 839, 993, 463, 1883, 531, 1571, 503, 819, 523
Offset: 1

Views

Author

Omar E. Pol, Sep 03 2011

Keywords

Examples

			a(1) = 2+3+5 = 10.
a(2) = 3+5+7 = 15.
a(3) = 7+13+19 = 39.
a(4) = 5+13+17 = 35.
a(5) = 11+31+41 = 83.
a(6) = 7+13+19 = 39.

Links

Crossrefs

Cf. A077318, A132810, A193873, A194266.

Programs

  • Mathematica
    Table[ps = Select[Table[n*k + 1, {k, 100}], PrimeQ, 3]; If[Length[ps] == 3, Total[ps], 0], {n, 100}] (* T. D. Noe, Oct 21 2011 *)

A194266 Smallest sum of two distinct primes of the form n*k+1.

Original entry on oeis.org

5, 8, 20, 18, 42, 20, 72, 58, 56, 42, 90, 50, 132, 72, 92, 114, 240, 56, 420, 102, 170, 90, 186, 170, 252, 132, 272, 142, 292, 92, 684, 290, 266, 240, 282, 110, 372, 420, 236, 282, 822, 170, 604, 442, 452, 186, 942, 290, 688, 252, 410, 210, 850, 272, 992
Offset: 1

Views

Author

Omar E. Pol, Sep 03 2011

Keywords

Examples

			a(1) = 2+3 = 5
a(2) = 3+5 = 8
a(3) = 7+13 = 20
a(4) = 5+13 = 18
a(5) = 11+31 = 42
a(6) = 7+13 = 20

Crossrefs

Cf. A077318, A132810, A194265, A194267.

Programs

  • Mathematica
    Table[ps = Select[Table[n*k + 1, {k, 100}], PrimeQ, 2]; If[Length[ps] == 2, Total[ps], 0], {n, 100}] (* T. D. Noe, Oct 21 2011 *)
Showing 1-5 of 5 results.

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