A087191 -id:A087191 - cp's OEIS frontend

A087190 Numbers n such that n^4-(n+1)^3 is prime.

3, 4, 5, 6, 7, 10, 12, 16, 17, 19, 25, 26, 28, 39, 55, 56, 58, 62, 67, 72, 75, 87, 91, 95, 96, 97, 102, 111, 114, 115, 116, 124, 126, 128, 132, 137, 152, 160, 161, 172, 181, 182, 184, 191, 198, 201, 205, 208, 209, 213, 214, 217, 220, 223, 227, 235, 237, 247, 248, 250

Offset: 1

Hugo Pfoertner, Aug 23 2003

			a(1)=3 because 3^4-(3+1)^3=81-64=17 is prime.

Vincenzo Librandi, Table of n, a(n) for n = 1..5000

Cf. A087191 primes of the form n^4-(n+1)^3.

[n: n in [3..300]| IsPrime(n^4-(n+1)^3)]; // Vincenzo Librandi, Jul 16 2012

lst={};Do[If[PrimeQ[n^4-(n+1)^3],AppendTo[lst,n]],{n,3,1000}];lst (* Vincenzo Librandi, Jul 16 2012 *)

is(n)=isprime(n^4-(n+1)^3) \\ Charles R Greathouse IV, Jun 05 2017

A171771 Primes of form n^6-(n+1)^5.

Original entry on oeis.org

971, 431441, 838949, 2614691, 6770161, 43845881, 570523321, 9244951889, 33640090481, 41402933641, 81303824909, 126165366289, 137240997911, 346860978491, 372445245449, 525200678549, 726938163649, 774170449439

Offset: 1

Ulrich Krug (leuchtfeuer37(AT)gmx.de), Dec 18 2009

nonn

(1) It is conjectured that sequence is infinite.

(2) p=97=prime(25) is the smallest prime such that (p-1)^6-p^5 and p^6-(p+1)^5 are primes.

			4^6-5^5=971 and 9^6-10^5=431441 are prime.

Leonard E. Dickson: History of the Theory of numbers, vol. I, Dover Publications 2005
Derrick H. Lehmer, Guide to Tables in the Theory of Numbers Washington, D.C. 1941

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Cf. A002327, A140719, A087191

Select[Table[n^6-(n+1)^5,{n,3,100}],PrimeQ] (* Harvey P. Dale, Mar 06 2019 *)

Edited by D. S. McNeil, Nov 21 2010

A172192 Numbers k such that k^6 - (k+1)^5 is prime.

Original entry on oeis.org

4, 9, 10, 12, 14, 19, 29, 46, 57, 59, 66, 71, 72, 84, 85, 90, 95, 96, 97, 114, 119, 122, 155, 157, 190, 191, 204, 207, 212, 221, 222, 244, 251, 256, 276, 285, 286, 289, 294, 300, 301, 307, 319, 320, 337, 344, 355, 359, 380, 382, 392, 400, 411, 422, 426, 441, 451

Offset: 1

Ulrich Krug (leuchtfeuer37(AT)gmx.de), Jan 29 2010

Corresponding primes are in A171771. Negative values of primes are obtained for 1 and 2.

			4^6-(4+1)^5 = 971 is prime, so 4 is in the sequence.
5^6-(5+1)^5 = 7849 = 47*167 is composite, so 5 is not in the sequence.
9^6-(9+1)^5 = 431441 is prime, so 9 is in the sequence.

Cf. A171771, A002327 (primes of form n^2-n-1), A140719 (primes of form n^3-(n+1)^2), A087191 (primes of form n^4-(n+1)^3).

[ n: n in [1..460] | IsPrime(p) and p gt 0 where p is n^6-(n+1)^5 ];

Select[Range[3,500],PrimeQ[#^6-(#+1)^5]&] (* Harvey P. Dale, Apr 25 2011 *)

is(n)=isprime(n^6-(n+1)^5) \\ Charles R Greathouse IV, Jun 13 2017

Edited, extended, non-specific references removed and MAGMA program added by Associate Editors OEIS, Mar 05 2010

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A087190 Numbers n such that n^4-(n+1)^3 is prime.

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A171771 Primes of form n^6-(n+1)^5.

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A172192 Numbers k such that k^6 - (k+1)^5 is prime.

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Author

Keywords

Comments

Examples

Crossrefs

Programs

Magma

Mathematica

PARI

Extensions