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
Keywords
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
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
Comments