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.

A180493 Numbers n such that prime(n)! is divisible by A180491(prime(n)).

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 21, 22, 23, 24, 25, 26, 27, 29, 30, 35, 38, 39, 40, 53
Offset: 1

Views

Author

Carl R. White, Sep 08 2010

Keywords

Comments

Also numbers n such that prime(n)! is divisible by A180492(n).
Is this sequence finite?
From Robert G. Wilson v, Sep 09 2010: (Start)
Checked to 10000 for more terms.
Conjecture: This sequence is finite and all its terms are present. (End)

Crossrefs

Cf. A034386, A000142, A004125, A180491, A180492.

Programs

  • Mathematica
    f[n_] := Times @@ Mod[n, Range[2, n - 1]]; k = 1; lst = {}; While[k < 10001, If[ Divisible[ Prime@k!, f@Prime@k], AppendTo[lst, k]; Print@k]; k++ ]; lst (* Robert G. Wilson v, Sep 09 2010 *)

A180492 Product of remainders of prime(n) mod k, for k = 2,3,4,...,prime(n)-1.

Original entry on oeis.org

1, 1, 2, 6, 720, 2160, 2419200, 65318400, 754427520000, 32953394073600000, 311409573995520000, 37269497815783833600000, 7890485108998805913600000000, 1096106738916569123487744000000, 4067286739206415827555188736000000000, 7924734685010508814047938347008000000000000
Offset: 1

Views

Author

Carl R. White, Sep 08 2010

Keywords

Comments

Nonzero entries in A180491. Note that this sequence, while increasing in general, is not strictly increasing.
a(n) is divisible by (n-1)!. - Robert G. Wilson v, Sep 09 2010

Examples

			Since prime(4) = 7, a(4) = (7 mod 2) * (7 mod 3) * (7 mod 4) * (7 mod 5) * (7 mod 6) = 1 * 1 * 3 * 2 * 1 = 6.

Crossrefs

Cf. A034386, A000142, A004125, A180491, A180493.
Cf. A173392, A000040.

Programs

  • Maple
    a:= n-> (p-> mul(irem(p, k), k=2..p-1))(ithprime(n)):
seq(a(n), n=1..17);  # Alois P. Heinz, Jul 16 2022
  • Mathematica
    f[n_]:=Times@@(Mod[n,# ]&/@ Range[2,n-1]); Table[f[Prime[i]],{i,20}] (* Harvey P. Dale, Sep 18 2010 *)
f[n_] := Times @@ Mod[n, Range[2, n - 1]]; Table[ f@ Prime@ n, {n, 10}] (* Robert G. Wilson v, Sep 09 2010 *)

Formula

a(n) = A173392(A000040(n)) = A180491(A000040(n)). - Ridouane Oudra, Nov 01 2024

A283616 a(n) = Product_{k=2..floor(sqrt(2n-1)/2)+1} (2n-1) mod (2k-1).

Original entry on oeis.org

1, 1, 2, 1, 0, 2, 1, 0, 4, 4, 0, 6, 0, 0, 8, 1, 0, 0, 4, 0, 12, 3, 0, 20, 0, 0, 24, 0, 0, 24, 5, 0, 0, 32, 0, 16, 9, 0, 0, 56, 0, 72, 0, 0, 320, 0, 0, 0, 84, 0, 24, 240, 0, 512, 160, 0, 90, 0, 0, 0, 0, 0, 0, 12, 0, 500, 0, 0, 160, 672, 0, 0, 0, 0, 2880, 1792, 0, 0, 72, 0, 0, 378
Offset: 1

Views

Author

Zhandos Mambetaliyev, Mar 11 2017

Keywords

Comments

For n>1, if a(n) > 0 then 2n-1 is prime.
From Robert G. Wilson v, Mar 15 2017: (Start)
Except for n=1, a(n)=0 iff 2n-1 is not prime (A104275).
a(n) is prime for n: 3, 6, 22 & 31. (End)

Links

Crossrefs

Cf. A180491.

Programs

  • Mathematica
    Table[Product[Mod[(2 n - 1), (2 k - 1)], {k, 2, Floor[Sqrt[2 n - 1]/2] + 1}], {n, 80}] (* Michael De Vlieger, Mar 15 2017 *)
  • PARI
    a(n)=my(t=2*n-1); prod(k=2,sqrtint(t\4)+1, t%(2*k-1)) \\ Charles R Greathouse IV, Mar 22 2017
Showing 1-3 of 3 results.

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

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