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.

A168550 Natural numbers k for which 1 + 2*k^3 is prime.

Original entry on oeis.org

1, 2, 5, 6, 9, 11, 12, 20, 21, 26, 27, 29, 30, 32, 35, 44, 57, 59, 60, 71, 72, 77, 86, 92, 95, 96, 99, 107, 111, 120, 134, 140, 149, 150, 152, 159, 162, 164, 165, 170, 185, 186, 191, 192, 197, 204, 221, 227, 231, 237, 246, 249, 252, 260, 264, 266, 269, 275, 290, 297
Offset: 1

Views

Author

Juri-Stepan Gerasimov, Nov 29 2009

Keywords

Examples

			20 is a term because 1 + 2*20^3 = 16001 is prime.

Links

Crossrefs

Cf. A201107, A033562, A049408.

Programs

  • Maple
    isA168550 := proc(n) isprime(1+2*n^3) ; end proc: for n from 1 to 400 do if isA168550(n) then printf("%d,",n) ; end if; end do: # R. J. Mathar, Nov 30 2009
  • Mathematica
    Select[Range[300],PrimeQ[1+2#^3]&] (* Harvey P. Dale, Jan 13 2022 *)

Extensions

Terms beyond 21 from R. J. Mathar, Nov 30 2009
Example corrected by Jon E. Schoenfield, May 11 2019

A230506 Numbers n with 2*n + 1 and 2*n^3 + 1 both prime.

Original entry on oeis.org

1, 2, 5, 6, 9, 11, 20, 21, 26, 29, 30, 35, 44, 86, 95, 96, 99, 111, 120, 134, 140, 165, 186, 191, 204, 221, 231, 249, 260, 299, 321, 330, 354, 375, 380, 384, 386, 431, 440, 455, 485, 491, 506, 515, 545, 551, 554, 596, 600, 629
Offset: 1

Views

Author

Zhi-Wei Sun, Oct 21 2013

Keywords

Comments

This sequence is interesting because of the conjecture in the comments in A230507.

Examples

			a(1) = 1 since 2*1 + 1 = 2*1^3 + 1 = 3 is a prime.
a(2) = 2 since 2*2 + 1 = 5 and 2*2^3 + 1 = 17 are both prime.

Links

Crossrefs

Cf. A000040, A005097, A201107, A230507.

Programs

  • Mathematica
    q[n_]:=PrimeQ[2n+1]&&PrimeQ[2n^3+1]
m=0
Do[If[q[n],m=m+1;Print[m," ",n]],{n,1,629}]

A309856 Primes of the form 2*p^3+1 where p is also prime.

Original entry on oeis.org

17, 251, 2663, 48779, 410759, 715823, 2450087, 6615899, 13935743, 15290747, 23394167, 38930219, 160125983, 219804479, 236741543, 1258845587, 1666475243, 2116179719, 2308641299, 3604970627, 3991233959, 4283401139, 6109873703, 8207369603, 8487319319, 9264815927
Offset: 1

Views

Author

R. J. Mathar, Aug 20 2019

Keywords

Comments

All terms == 5 (mod 6).

Links

Crossrefs

Cf. A309857.
Subsequence of A214175 and of A201107.

Programs

  • Maple
    f:= proc(n) if isprime(n) and isprime(2*n^3+1) then return 2*n^3+1 fi end proc:
map(f, [2,seq(i,i=5..10000,6)]);# Robert Israel, Aug 22 2019
  • Mathematica
    pp = Join[{2}, Select[Range[5, 10000, 6], PrimeQ[#] && PrimeQ[2#^3 + 1]&]];
2 pp^3 + 1 (* Jean-François Alcover, Jul 31 2020 *)
Select[2*Prime[Range[300]]^3+1,PrimeQ] (* Harvey P. Dale, Dec 09 2024 *)

Formula

a(n) = 1+2*A309857(n)^3.
Showing 1-3 of 3 results.

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

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