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.

A162488 Numbers x such that x^y + y^x is prime, for some y>1, y

Original entry on oeis.org

3, 9, 15, 21, 24, 32, 33, 38, 54, 56, 68, 69, 75, 76, 81, 87, 114, 122, 135, 144, 158, 160, 171, 185, 206, 214, 215, 235, 237, 248, 318, 322, 333, 343, 357, 387, 405, 406, 422, 425, 435, 436, 444, 471, 477, 488, 510, 519, 545, 557, 580, 590, 636, 648, 663, 675
Offset: 1

Views

Author

M. F. Hasler, Jul 04 2009

Keywords

Comments

This sequence lists the values occurring in A162486.
Sequences A162489 and A162490 list the corresponding (smallest possible) y values and primes.
See the main entry A094133 for more information, links and references.
Some terms could appear more than once, such as 114, 318 & 590. - Robert G. Wilson v, Aug 17 2009

Examples

			The least x such that x^y + y^x is prime for some y>1, y<x is a(1)=3, the smallest such y is a(1)=2, yielding the prime A162490(1) = 9 + 8 = 17.
The least x > a(4)=21 such that x^y + y^x is prime for some y<x, y>1, is a(5)=24, yielding the prime A162490(5) for y=A162489(5)=5, while A162486(5)=33, yielding the smaller prime A094133(5)=8589935681 with y=A162487(5), comes only after a(6)=32.

Crossrefs

Cf. A094133, A160044 (complement of this sequence), A162486 - A162490.

Programs

  • Mathematica
    lst = {}; Do[ If[ PrimeQ[x^y + y^x], AppendTo[lst, x]], {x, 3, 680}, {y, 2, x - 1}]; Union@ lst (* Robert G. Wilson v, Aug 17 2009 *)
  • PARI
    for(i=3,999,for(j=2,i-1,is/*pseudo*/prime(i^j+j^i)|next;print1(i", ");break))

Formula

a(n)^A162489(n) + A162489(n)^a(n) = A162490(n).

Extensions

More terms from Robert G. Wilson v, Aug 17 2009

A162486 Values of x for A094133: primes of the form x^y + y^x, x > y > 1.

Original entry on oeis.org

3, 9, 15, 21, 33, 24, 56, 32, 54, 38, 69, 76, 68, 75, 122, 87, 81, 135, 114, 114, 144, 158, 185, 160, 171, 206, 422, 215, 357, 519, 214, 248, 237, 235, 2007, 471, 318, 2127, 322, 333, 1036, 318, 387, 477, 435, 343, 425, 406, 782, 405, 717, 3759, 444, 436, 773, 636
Offset: 1

Views

Author

M. F. Hasler, Jul 04 2009

Keywords

Comments

See A162488 for the list of all numbers occurring in this sequence.
See A094133 for links and references.

Formula

A094133(n) = A162486(n)^A162487(n) + A162487(n)^A162486(n).

Extensions

More terms from Jinyuan Wang, Mar 03 2020

A162489 Least y such that x^y + y^x is prime, for x = A162488(n).

Original entry on oeis.org

2, 2, 2, 2, 5, 15, 2, 33, 7, 3, 21, 8, 34, 9, 80, 56, 67, 9, 32, 65, 45, 133, 98, 36, 51, 157, 76, 214, 200, 87, 91, 111, 122, 342, 20, 142, 364, 289, 9, 184, 98, 423, 365, 20, 56, 441, 329, 8, 234, 234, 157, 291, 91, 379, 98, 464, 518, 325, 32, 654, 87, 634, 34, 21, 443
Offset: 1

Views

Author

M. F. Hasler, Jul 04 2009

Keywords

Comments

Sequences A162488 and A162490 list the corresponding x values and primes.
See there and the main entry A094133 for more information, links and references.

Examples

			The least x such that x^y + y^x is prime for some x>y>1 is A162488(1)=3, the smallest such y is a(1)=2, yielding the prime A162490(1) = 9 + 8 = 17.

Crossrefs

Cf. A094133, A162486, A162487, A162488, A162490.

Programs

  • Mathematica
    lst = {}; Do[ If[ PrimeQ[x^y + y^x], AppendTo[lst, {x, y}]], {x, 3, 750}, {y, 2, x - 1}]; Transpose[ lst][[2]] (* Robert G. Wilson v, Aug 17 2009 *)
  • PARI
    for(i=3,999,for(j=2,i-1,isprime(i^j+j^i)||next;print1(j", ");break))

Formula

a(n)^A162488(n)+A162488(n)^a(n) = A162490(n)

Extensions

More terms from Robert G. Wilson v, Aug 17 2009
Showing 1-3 of 3 results.

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