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.

A245042 Primes of the form (k^2+4)/5.

Original entry on oeis.org

17, 73, 89, 193, 337, 521, 953, 1009, 1249, 1657, 2377, 2833, 3329, 3433, 4441, 4561, 5849, 6553, 7297, 8081, 8737, 9769, 11617, 12401, 12601, 13417, 15569, 16937, 17881, 18121, 20353, 21649, 27529, 28729, 29033, 30577, 33457, 35449, 36809, 46273, 49801
Offset: 1

Views

Author

Chai Wah Wu, Jul 10 2014

Keywords

Comments

Also equal to primes p such that 5*p-4 is a perfect square.

Links

Crossrefs

Cf. A154418.
Cf. A154616, A002327, A066436.

Programs

  • Mathematica
    Select[(Range[500]^2+4)/5,PrimeQ] (* Harvey P. Dale, Jul 13 2014 *)
  • Python
    import sympy
L = (k**2 + 4 for k in range(10**3))
[n//5 for n in L if n % 5 == 0 and sympy.ntheory.isprime(n//5)]

A154419 Primes of the form 20*k^2 + 36*k + 17.

Original entry on oeis.org

17, 73, 953, 1249, 2377, 2833, 3329, 4441, 8737, 12401, 13417, 15569, 17881, 20353, 21649, 28729, 33457, 36809, 49801, 51817, 62497, 67049, 71761, 74177, 86857, 89513, 100537, 103393, 118273, 121369, 127681, 134153, 144161, 161641, 168913
Offset: 1

Views

Author

Vincenzo Librandi, Jan 09 2009

Keywords

Comments

Also primes of the form 5*j^2 + 18*j + 17. (Proof: this format implies that j=2*k, even, because otherwise 5*j^2 + 18*j + 17 is even and cannot be prime. So 5*j^2 + 18*j + 17 = 20*k^2 + 36*k + 17.) - R. J. Mathar, Jan 12 2009

Links

Crossrefs

Cf. A017377, A154418.

Programs

  • Magma
    [a: n in [0..100] | IsPrime(a) where a is 20*n^2+36*n+17]; // Vincenzo Librandi, Jul 23 2012
  • Mathematica
    Select[Table[20n^2+36n+17,{n,0,6001}],PrimeQ] (* Vincenzo Librandi, Jul 23 2012 *)
  • PARI
    select(isprime, vector(100, n, 20*(n-1)^2 + 36*(n-1) + 17)) \\ Robert C. Lyons,  Feb 27 2025

A338175 Primes p such that (p^2+6)/5 is prime.

Original entry on oeis.org

2, 3, 7, 17, 23, 47, 53, 157, 173, 193, 233, 347, 353, 373, 383, 443, 457, 577, 823, 857, 907, 1117, 1153, 1193, 1223, 1277, 1447, 1453, 1523, 1697, 1733, 1823, 1873, 2027, 2153, 2203, 2293, 2333, 2357, 2467, 2557, 2657, 2683, 2707, 2777, 2797, 2803, 2903, 3217, 3253, 3323, 3407, 3433, 3643, 3673
Offset: 1

Views

Author

J. M. Bergot and Robert Israel, Oct 14 2020

Keywords

Comments

All terms end in 2, 3 or 7.

Examples

			a(3)=7 is a member because 7 is prime and (7^2+6)/5 = 11 is prime.

Links

Crossrefs

Cf. A154418.

Programs

  • Maple
    select(p -> isprime(p) and isprime((p^2+6)/5), [2,seq(seq(10*i+j,j=[3,7]),i=0..1000)]);
Showing 1-3 of 3 results.

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

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