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A226777
Higher powers that are sums of two distinct higher powers.
4
243, 2744, 6561, 177147, 185193, 474552, 614656, 810000, 941192, 1124864, 1419857, 1500625, 3241792, 4782969, 7962624, 11239424, 16003008, 17850625, 21952000, 26873856, 28372625, 52200625, 68574961, 82312875, 117649000, 129140163, 162771336, 200201625, 238328000
OFFSET
1,1
COMMENTS
x is in the sequence iff there are distinct y,z such that x = y + z and x,y,z are all in A076467.
LINKS
Robert Israel and Reinhard Zumkeller, Table of n, a(n) for n = 1..1000 (first 264 terms from Robert Israel)
EXAMPLE
243 is in the sequence because 243 = 3^5 = 3^3 + 6^3.
MAPLE
N := 10^12: # to get terms up to N
S := {seq(seq(a^x, a=1 .. floor(N^(1/x))), x = 3 .. floor(log[2](N)))}:
f:= proc(n) local L; L:= S[1..n-1] minus {S[n]/2}; nops(map2(`-`, S[n], L) intersect L) > 0 end proc;
A:= map(t -> S[t], select(f, [$1..nops(S)]));
MATHEMATICA
max = 3*10^8; pp = Join[{1}, Table[n^k, {k, 3, Floor[Log[2, max]]}, {n, 2, Floor[max^(1/k)]}] // Flatten // Union]; Select[Total /@ Subsets[pp, {2}], MemberQ[pp, #]&] // Union (* Jean-François Alcover, Feb 14 2018 *)
PROG
(Haskell)
import qualified Data.Set as Set (null, split, filter)
import Data.Set (Set, empty, insert, member)
a226777 n = a226777_list !! (n-1)
a226777_list = f a076467_list empty where
f (x:xs) s | Set.null $ Set.filter ((`member` s) . (x -)) s'
= f xs (x `insert` s)
| otherwise = x : f xs (x `insert` s)
where (s', _) = Set.split (x `div` 2) s
-- Reinhard Zumkeller, Sep 13, Jun 19 2013
CROSSREFS
Sequence in context: A100627 A269056 A209507 * A016757 A133550 A029700
KEYWORD
nonn
AUTHOR
Robert Israel, Jun 17 2013
STATUS
approved