A218346 - OEIS

%I #18 May 28 2021 23:02:53

%S 5,28,31,257,260,283,3126,3129,3152,3381,46657,46660,46683,46912,

%T 49781,823544,823547,823570,823799,826668,870199,16777217,16777220,

%U 16777243,16777472,16780341,16823872,17600759,387420490,387420493,387420516,387420745,387423614,387467145

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

%C Subsequence of A066846.

%H Robert Israel, <a href="/A218346/b218346.txt">Table of n, a(n) for n = 1..10000</a>

%e a(1) = 2^2 + 1^1 = 5,

%e a(2) = 3^3 + 1^1 = 28,

%e a(3) = 2^2 + 3^3 = 31.

%p N:= 10^12: # for terms <= N

%p S:= NULL:

%p for m from 1 do v:= m^m; if v > N then break fi; S:= S,v od:

%p 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

%t 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 *)

%o (Python)

%o from itertools import count, takewhile

%o def aupto(lim):

%o   pows = list(takewhile(lambda x: x < lim, (i**i for i in count(1))))

%o   sums = (aa+bb for i, bb in enumerate(pows) for aa in pows[i+1:])

%o   return sorted(set(s for s in sums if s <= lim))

%o print(aupto(387467145))  # _Michael S. Branicky_, May 28 2021

%Y Cf. A000312, A066846, A218347.

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

%K nonn

%O 1,1

%A _Alex Ratushnyak_, Oct 26 2012