A226777 Higher powers that are sums of two distinct higher powers.

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

Adjacent sequences: A226774 A226775 A226776 * A226778 A226779 A226780

Keyword

nonn

Author

Robert Israel, Jun 17 2013

Status

approved