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.

A118752 a(n) = product[k=0..n] P(k), where P(k) is the smallest prime > 3*n. a(n) = product[k=0..n] A118751(k).

Original entry on oeis.org

2, 10, 70, 770, 10010, 170170, 3233230, 74364290, 2156564410, 62540367890, 1938751404590, 71733801969830, 2654150672883710, 108820177588232110, 4679267636293980730, 219925578905817094310, 11656055682008305998430
Offset: 0

Views

Author

Jonathan Vos Post, Apr 29 2006

Keywords

Comments

Analogous to A118456 a(n) = product{k=1..n} P(k), where P(k) is the smallest prime >= k.

Links

Crossrefs

Cf. A020482, A049653, A060266-A060268, A060264, A060265, A060308, A118455, A118456, A118748-51.

Programs

  • Mathematica
    Rest[FoldList[Times,1,Table[NextPrime[3n],{n,0,20}]]] (* Harvey P. Dale, Mar 09 2014 *)

Extensions

Definition corrected by Harvey P. Dale, Mar 09 2014

A118749 Largest prime <= 3*n.

Original entry on oeis.org

3, 5, 7, 11, 13, 17, 19, 23, 23, 29, 31, 31, 37, 41, 43, 47, 47, 53, 53, 59, 61, 61, 67, 71, 73, 73, 79, 83, 83, 89, 89, 89, 97, 101, 103, 107, 109, 113, 113, 113, 113, 113, 127, 131, 131, 137, 139, 139, 139, 149, 151, 151, 157, 157, 163, 167, 167, 173, 173, 179, 181
Offset: 1

Views

Author

Jonathan Vos Post, Apr 29 2006

Keywords

Comments

Analogous to A060308 largest prime <= 2*k.

Crossrefs

Cf. A007917 (largest prime <= n), A008585 (3n).
Cf. A060308, A118750, A118751, A118752.
Essentially the same as A081259.

Programs

  • Magma
    [NthPrime(#PrimesUpTo(3*n)): n in [1..100]]; // Vincenzo Librandi, Nov 25 2015
  • Mathematica
    Table[Max[FactorInteger[(3 n)!/(n!)^3]], {n, 1, 70}] (* Vincenzo Librandi, Nov 25 2015 *)
NextPrime[3*Range[70]+1,-1] (* Harvey P. Dale, Nov 12 2017 *)
  • PARI
    vector(100, n, precprime(3*n)) \\ Altug Alkan, Nov 25 2015

Formula

a(n) = A007917(A008585(n)). - Michel Marcus, Nov 25 2015

A118753 First prime after 4n. Smallest prime >= 4*n. Bisection of A060264.

Original entry on oeis.org

2, 5, 11, 13, 17, 23, 29, 29, 37, 37, 41, 47, 53, 53, 59, 61, 67, 71, 73, 79, 83, 89, 89, 97, 97, 101, 107, 109, 113, 127, 127, 127, 131, 137, 137, 149, 149, 149, 157, 157, 163, 167, 173, 173, 179, 181, 191, 191, 193, 197, 211, 211, 211, 223, 223, 223, 227, 229, 233
Offset: 0

Views

Author

Jonathan Vos Post, Apr 29 2006

Keywords

Comments

Analogous to A060264 First prime after 2n; A118751 First prime after 3n.

Links

Crossrefs

Cf. A000040, A008586, A060308, A060264, A118747-56.

Programs

  • Maple
    seq(nextprime(4*k),k=0..100); # Robert Israel, Dec 25 2017
  • Mathematica
    NextPrime/@(4Range[0,60]) (* Harvey P. Dale, Nov 14 2021 *)

Formula

a(n) = min{A008586(n)+k such that k>0 and A008586(n)+k in A000040}.
Showing 1-3 of 3 results.

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

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