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 1-2 of 2 results.

A066846 Numbers of the form a^a + b^b, a >= b > 0.

Original entry on oeis.org

2, 5, 8, 28, 31, 54, 257, 260, 283, 512, 3126, 3129, 3152, 3381, 6250, 46657, 46660, 46683, 46912, 49781, 93312, 823544, 823547, 823570, 823799, 826668, 870199, 1647086, 16777217, 16777220, 16777243, 16777472, 16780341, 16823872, 17600759, 33554432
Offset: 0

Views

Author

Leroy Quet, Jan 20 2002

Keywords

Examples

			28 is included because 28 = 1^1 + 3^3.
		

Crossrefs

Cf. A068145: primes of the form a^a + b^b.

Programs

  • Mathematica
    nn = 10; Select[Union[Flatten[Table[a^a + b^b, {a, nn}, {b, a, nn}]]], # <= nn^nn + 1 &] (* T. D. Noe, Nov 15 2012 *)

Extensions

Name improved by Alex Ratushnyak, Oct 26 2012

A218346 Numbers of the form a^a + b^b, with a > b > 0.

Original entry on oeis.org

5, 28, 31, 257, 260, 283, 3126, 3129, 3152, 3381, 46657, 46660, 46683, 46912, 49781, 823544, 823547, 823570, 823799, 826668, 870199, 16777217, 16777220, 16777243, 16777472, 16780341, 16823872, 17600759, 387420490, 387420493, 387420516, 387420745, 387423614, 387467145
Offset: 1

Views

Author

Alex Ratushnyak, Oct 26 2012

Keywords

Comments

Subsequence of A066846.

Examples

			a(1) = 2^2 + 1^1 = 5,
a(2) = 3^3 + 1^1 = 28,
a(3) = 2^2 + 3^3 = 31.
		

Crossrefs

Cf. A068145: primes of the form a^a + b^b.

Programs

  • Maple
    N:= 10^12: # for terms <= N
    S:= NULL:
    for m from 1 do v:= m^m; if v > N then break fi; S:= S,v od:
    sort(convert(select(`<=`,{seq(seq(S[i]+S[j],j=i+1..m-1),i=1..m-1)},N),list)); # Robert Israel, Aug 10 2020
  • Mathematica
    nn = 10; Select[Union[Flatten[Table[a^a + b^b, {a, nn}, {b, a + 1, nn}]]], # <= nn^nn + 1 &] (* T. D. Noe, Nov 15 2012 *)
  • Python
    from itertools import count, takewhile
    def aupto(lim):
      pows = list(takewhile(lambda x: x < lim, (i**i for i in count(1))))
      sums = (aa+bb for i, bb in enumerate(pows) for aa in pows[i+1:])
      return sorted(set(s for s in sums if s <= lim))
    print(aupto(387467145))  # Michael S. Branicky, May 28 2021
Showing 1-2 of 2 results.