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.

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

A138905 a(n) is n-th prime == -1 (mod 6n).

Original entry on oeis.org

5, 23, 71, 167, 179, 431, 461, 863, 863, 839, 1583, 1511, 1949, 2099, 2339, 4127, 4283, 4751, 4673, 4919, 5669, 6599, 8693, 10079, 7349, 10607, 12149, 11087, 12527, 11159, 15809, 19583, 16829, 19583, 13859, 25703, 24197, 25307, 23633, 21839, 34439
Offset: 1

Views

Author

Zak Seidov, Apr 03 2008

Keywords

Examples

			a(1) = 1st term in A007528 (Primes of form 6n-1)
a(2) = 2nd term in A068231 (Primes congruent to 11 (mod 12))
a(3) = 3rd term in A061242 (Primes of form 18n-1)
a(4) = 4th term in A134517 (Primes of form 24n-1)
a(5) = 5th term in A132236 (Primes congruent to 29 (mod 30))

Links

Crossrefs

Cf. A007528, A061242, A068231, A093871, A132236, A134517, A138906, A138907.

Programs

  • Mathematica
    a[n_]:=Module[{p=1,cnt=0},Until[cnt==n,If[Mod[Prime[p],6n]==6n-1,cnt++];p++];Prime[p-1]];Array[a,41] (* James C. McMahon, Jun 22 2025 *)

A093870 Triangle read by rows: T(n,k) is the k-th prime = -1 (mod n), 1 <= k <= n.

Original entry on oeis.org

2, 3, 5, 2, 5, 11, 3, 7, 11, 19, 19, 29, 59, 79, 89, 5, 11, 17, 23, 29, 41, 13, 41, 83, 97, 139, 167, 181, 7, 23, 31, 47, 71, 79, 103, 127, 17, 53, 71, 89, 107, 179, 197, 233, 251, 19, 29, 59, 79, 89, 109, 139, 149, 179, 199, 43, 109, 131, 197, 241, 263, 307, 373, 439, 461, 571
Offset: 1

Views

Author

Amarnath Murthy, Apr 20 2004

Keywords

Examples

			2;
3,5;
2,5,11;
3,7,11,19;
...

Crossrefs

Cf. A077316, A038700 (first column), A093871 (main diagonal).

Programs

  • Mathematica
    row[n_] := Reap[Module[{k, p}, For[k = 0; p = n - 1, k < n, p += n, If[PrimeQ[p], k++; Sow[p]]]]][[2, 1]];
Array[row, 12] // Flatten (* Jean-François Alcover, Jun 08 2020 *)

Extensions

Edited and extended by Franklin T. Adams-Watters, Aug 29 2006
Definition clarified by Zak Seidov, Apr 16 2013
Duplicate term 139 removed by Jean-François Alcover, Jun 08 2020
Showing 1-3 of 3 results.

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

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