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

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

Author

Alex Ratushnyak, Oct 26 2012

Keywords

• nonn

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.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000312, A066846, A218347.

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