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.

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A097499 Numbers of the form p^q + q^p where p and q are consecutive primes.

Original entry on oeis.org

17, 368, 94932, 1996813914, 36314872537968, 8660320497414243870, 244552822542936127033092, 257904243416235317958787975746, 3091062959814255272215316579358416079052
Offset: 1

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Author

Cino Hilliard, Aug 24 2004

Keywords

Comments

The first term is the only prime in the sequence.

Crossrefs

Programs

  • Mathematica
    lst={}; Do[p=Prime[n]; q=Prime[n+1]; a=p^q+q^p; AppendTo[lst,a],{n,4!}]; lst (* Vladimir Joseph Stephan Orlovsky, Aug 16 2009 *)
    First[#]^Last[#]+Last[#]^First[#]&/@Partition[Prime[Range[10]],2,1] (* Harvey P. Dale, Sep 20 2011 *)
  • PARI
    f(n) = for(x=1,n,p=prime(x);q=prime(x+1);v=p^q+q^p;print1(v","))

Formula

a(n) = A053089(n) + A078422(n). - Amiram Eldar, Jul 07 2024

Extensions

Offset corrected by Amiram Eldar, Jul 07 2024

A332849 a(n) = prime(n)^prime(n+1) + prime(n) + prime(n+1).

Original entry on oeis.org

13, 251, 78137, 1977326761, 34522712143955, 8650415919381337963, 239072435685151324847189, 257829627945307727248226067301, 3091058643093537522799545838540043339115, 2159424054808578564166497528588784562372597489, 15148954872646847105498509334067131813327318808179940579
Offset: 1

Views

Author

J. M. Bergot and Robert Israel, Feb 26 2020

Keywords

Comments

a(n) is prime for n = 1,2,3,4, but for no other n < 500.
On the other hand, prime(n+1)^prime(n)+prime(n)+prime(n+1) is not prime for n < 500. - Robert Israel, Feb 27 2020

Examples

			a(3) = 5^7 + 5 + 7 = 78137.
		

Crossrefs

Programs

  • Maple
    seq(ithprime(i)^ithprime(i+1)+ithprime(i)+ithprime(i+1),i=1..20);
  • Mathematica
    Map[#[[1]]^#[[2]]+Total[#]&,Partition[Prime[Range[15]],2,1]] (* Paolo Xausa, Nov 02 2023 *)

Formula

a(n) = A053089(n) + A001043(n). - Omar E. Pol, Feb 26 2020

A321663 a(n) = prime(n)^prime(n+2).

Original entry on oeis.org

32, 2187, 48828125, 96889010407, 505447028499293771, 1461920290375446110677, 19967568900859523802559065713, 12129821994589221844500501021364910179, 1635170022196481349560959748587682926364327, 1284475787728524720826927656893473276744000042113841709
Offset: 1

Views

Author

Kei Ryan, Nov 16 2018

Keywords

Examples

			a(3)=48828125 because 5 is the 3rd prime, 11 is the 5th prime and 5^11=48828125.
		

Crossrefs

Cf. A053089 (prime(n)^prime(n+1)), A000040.

Programs

  • Mathematica
    Array[Prime[#]^Prime[# + 2] &, 10] (* Michael De Vlieger, Nov 25 2018 *)
    #[[1]]^#[[3]]&/@Partition[Prime[Range[20]],3,1] (* Harvey P. Dale, Jun 20 2023 *)

Formula

a(n) = prime(n)^prime(n+2).
Previous Showing 11-13 of 13 results.