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.

A383241 a(n) = p(n)*p(n+1)*(p(n+1) - p(n)) - 1, where p(n) = prime(n).

Original entry on oeis.org

5, 29, 69, 307, 285, 883, 645, 1747, 4001, 1797, 6881, 6067, 3525, 8083, 14945, 18761, 7197, 24521, 19027, 10365, 34601, 26227, 44321, 69063, 39187, 20805, 44083, 23325, 49267, 200913, 66547, 107681, 38085, 207109, 44997, 142241, 153545, 108883, 173345
Offset: 1

Views

Author

Clark Kimberling, May 07 2025

Keywords

Examples

			a(n) = A383242(n) - 2.

Crossrefs

Cf. A000042, A383242, A383243, A383244.

Programs

  • Mathematica
    z = 60; p[n_] := Prime[n];
f[n_] := p[n]*p[n + 1]*(p[n + 1] - p[n])
Table[f[n] - 1, {n, 1, z}]  (* A383241 *)
Table[f[n] + 1, {n, 1, z}]  (* A383242 *)

A383243 Primes of the form p(k)*p(k+1)*(p(k+1) - p(k)) - 1 sorted by increasing k.

Original entry on oeis.org

5, 29, 307, 883, 1747, 4001, 6067, 26227, 108883, 152083, 424481, 311347, 396883, 848201, 580627, 1713709, 1814509, 864883, 5092973, 3046789, 3386989, 1664083, 2581961, 2196307, 2304307, 2377747, 6955309, 3526867, 4088467, 20916053, 4796083, 7339361
Offset: 1

Views

Author

Clark Kimberling, May 07 2025

Keywords

Comments

Conjecture: there are infinitely many such primes.

Crossrefs

Cf. A000042, A383242, A383244.
Primes in A383241.

Programs

  • Maple
    q:= 2; R:= NULL: count:= 0:
while count < 100 do
  p:= q;
  q:= nextprime(q);
  v:= p*q*(q-p)-1;
  if isprime(v) then R:= R,v; count:= count+1 fi;
od:
R; # Robert Israel, May 11 2025
  • Mathematica
    z = 200; p[n_] := Prime[n];
f[n_] := p[n]*p[n + 1]*(p[n + 1] - p[n])
t1 = Table[f[n] - 1, {n, 1, z}];    (* A383241 *)
t2 = Table[f[n] + 1, {n, 1, z}];    (* A383242 *)
Select[t1, PrimeQ[#] &]  (* A383243 *)
Select[t2, PrimeQ[#] &]  (* A383244 *)

A383244 Primes of the form p(k)*p(k+1)*(p(k+1) - p(k)) + 1 sorted by increasing k.

Original entry on oeis.org

7, 31, 71, 647, 4003, 6883, 3527, 14947, 34603, 20807, 23327, 173347, 73727, 503869, 103967, 145799, 450403, 194687, 669283, 848203, 1193443, 1775563, 649799, 1976803, 2088547, 2131243, 4687069, 2534947, 2581963, 5338237, 3250123, 3411043, 1555847, 5346763
Offset: 1

Views

Author

Clark Kimberling, May 07 2025

Keywords

Comments

Conjecture: there are infinitely many such primes.

Crossrefs

Cf. A000042, A383241, A383243.
Primes in A383242.

Programs

  • Maple
    =q:= 2; R:= NULL: count:= 0:
while count < 100 do
  p:= q;
  q:= nextprime(q);
  v:= p*q*(q-p)+1;
  if isprime(v) then R:= R,v; count:= count+1 fi;
od:
R; # Robert Israel, May 11 2025
  • Mathematica
    z = 200; p[n_] := Prime[n];
f[n_] := p[n]*p[n + 1]*(p[n + 1] - p[n])
t1 = Table[f[n] - 1, {n, 1, z}];    (* A383241 *)
t2 = Table[f[n] + 1, {n, 1, z}];    (* A383242 *)
Select[t1, PrimeQ[#] &]  (* A383243 *)
Select[t2, PrimeQ[#] &]  (* A383244 *)
  • PARI
    select(isprime, vector(200, k, prime(k)*prime(k+1)*(prime(k+1) - prime(k)) + 1)) \\ Michel Marcus, May 12 2025
Showing 1-3 of 3 results.

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