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 1-4 of 4 results.

A056788 a(n) = n^n + (n-1)^(n-1).

Original entry on oeis.org

2, 5, 31, 283, 3381, 49781, 870199, 17600759, 404197705, 10387420489, 295311670611, 9201412118867, 311791207040509, 11414881932150269, 449005897206417391, 18884637964090410991, 845687005960046315793, 40173648337182874339601, 2017766063735610126699403
Offset: 1

Views

Author

Walter Nissen, Aug 20 2000

Keywords

Comments

For even n > 1, the absolute value of the discriminant of the polynomial x^n+x-1. [Corrected by Artur Jasinski, May 07 2010]
The largest known prime in this sequence is a(4) = 283.

Examples

			a(3) = 2^2 + 3^3 = 4 + 27 = 31.
		

References

  • R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 2, 1999; see equation (6.7).

Crossrefs

Cf. A000312 (n^n), A086797 (discriminant of the polynomial x^n-x-1).
Cf. A056187, A056790, A192397 (smallest & largest prime factor of a(n), records of the latter), A217435 = bigomega(a(n)).

Programs

  • Mathematica
    Join[{2}, Table[n^n+(n-1)^(n-1), {n, 2, 20}]] (* T. D. Noe, Aug 13 2004 *)
    Join[{2},Total/@Partition[Table[n^n,{n,20}],2,1]] (* Harvey P. Dale, Jun 26 2017 *)
  • PARI
    A056788(n)=n^n+(n-1)^(n-1)  \\ M. F. Hasler, Oct 02 2012

Extensions

Minor corrections by M. F. Hasler, Oct 02 2012

A056790 Greatest prime factor of n^n + (n+1)^(n+1).

Original entry on oeis.org

2, 5, 31, 283, 23, 743, 331, 1600069, 410353, 60042893, 8969, 7438489991, 116803, 4879633159, 61215157711, 338142271, 34041259347101651, 45072130459, 6564253087266573169, 22022174223585405703, 121937899012999, 69454092876521107983605569601, 5311242856728321929909
Offset: 0

Views

Author

Walter Nissen, Aug 20 2000

Keywords

Comments

Note that n^n + (n+1)^(n+1) = A056788(n+1).
Becomes "hard" (unknown) around n ~ 112, cf. link: As of today, even A217435(113) (number of prime factors) is unknown. - M. F. Hasler, Oct 04 2012
As of today, the first unknown term is a(143). - Daniel Suteu, Mar 11 2019

Examples

			a(4) = 23 because 4^4 + 5^5 = 3381 = 3 * 7^2 * 23.
		

Crossrefs

Programs

  • Mathematica
    Join[{2},FactorInteger[Total[#]][[-1,1]]&/@Partition[Table[n^n,{n,30}],2,1]] (* Harvey P. Dale, Apr 21 2018 *)
  • PARI
    A056790(n)=vecmax(factor((n+1)^(n+1)+n^n)[,1])  \\ M. F. Hasler, Oct 04 2012

Formula

a(n) = A006530(A056788(n+1)). - M. F. Hasler, Oct 04 2012

Extensions

a(0) = 2 added by Arkadiusz Wesolowski, Jun 30 2011
a(21)-a(22) added by Daniel Suteu, Mar 11 2019

A192397 Record holders for greatest prime factor of n^n + (n+1)^(n+1).

Original entry on oeis.org

2, 5, 31, 283, 743, 1600069, 60042893, 7438489991, 61215157711, 34041259347101651, 6564253087266573169, 22022174223585405703, 69454092876521107983605569601, 2360926164108571968813424783598971267, 462605180698333957063188362720170172617217, 14645575916792712592989131451003587034531413111, 214236369415820799335832514547376967536187180963
Offset: 1

Views

Author

Walter Nissen, Jun 29 2011

Keywords

Examples

			60042893 = A056790(9) is in the sequence because all earlier members of A056790 are smaller than 60042893.
		

Crossrefs

Programs

  • PARI
    fmax=0;for(k=0,35,my(x=factor(k^k+(k+1)^(k+1)),f=x[#x[,1],1]);if(f>fmax,print1(f,", ");fmax=f)) \\ Hugo Pfoertner, Aug 18 2019

Formula

A056790(m) < A056790(n), for all m < n

Extensions

2 added by Arkadiusz Wesolowski, Jun 30 2011

A309747 Numbers k such that k^k + (k+1)^(k+1) is a semiprime.

Original entry on oeis.org

5, 7, 9, 11, 14, 21, 37, 38, 39, 57, 90, 97, 162
Offset: 1

Views

Author

Hugo Pfoertner, Aug 15 2019

Keywords

Comments

Numbers k such that A217435(k+1) = 2.
a(14) >= 235, see FactorDB link.

Examples

			a(1) = 5 because 5^5 + 6^6 = 49781 = 67*743.
		

Crossrefs

Programs

  • PARI
    for(k=0,40,if(bigomega(k^k+(k+1)^(k+1))==2,print1(k,", ")))
Showing 1-4 of 4 results.