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A218346
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Numbers of the form a^a + b^b, with a > b > 0.
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3
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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
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OFFSET
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1,1
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COMMENTS
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LINKS
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EXAMPLE
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a(1) = 2^2 + 1^1 = 5,
a(2) = 3^3 + 1^1 = 28,
a(3) = 2^2 + 3^3 = 31.
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MAPLE
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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
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MATHEMATICA
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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 *)
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PROG
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(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))
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CROSSREFS
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Cf. A068145: primes of the form a^a + b^b.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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