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 A055394 Numbers that are the sum of a positive square and a positive cube. 49
 2, 5, 9, 10, 12, 17, 24, 26, 28, 31, 33, 36, 37, 43, 44, 50, 52, 57, 63, 65, 68, 72, 73, 76, 80, 82, 89, 91, 100, 101, 108, 113, 122, 126, 127, 128, 129, 134, 141, 145, 148, 150, 152, 161, 164, 170, 171, 174, 177, 185, 189, 196, 197, 204, 206, 208, 217, 220, 223 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS This sequence was the subject of a question in the German mathematics competition Bundeswettbewerb Mathematik 2017 (see links). The second round contained a question A4 which asks readers to "Show that there are an infinite number of a such that a-1, a, and a+1 are members of A055394". - N. J. A. Sloane, Jul 04 2017 and Oct 14 2017. LINKS Charles R Greathouse IV, Table of n, a(n) for n = 1..10000 Bundeswettbewerb Mathematik 2017, Der Wettbewerb in der 47 Runde Bundeswettbewerb Mathematik 2017, Aufgaben und Lösungen FORMULA a(n) >> n^(6/5). - Charles R Greathouse IV, May 15 2015 EXAMPLE a(5)=17 since 17=3^2+2^3. MAPLE isA055394 := proc(n)     local a, b;     for b from 1 do         if b^3 >= n then             return false;         end if;         asqr := n-b^3 ;         if asqr >= 0 and issqr(asqr) then             return true;         end if;     end do:     return; end proc: for n from 1 to 1000 do     if isA055394(n) then         printf("%d, ", n) ;     end if; end do: # R. J. Mathar, Dec 03 2015 MATHEMATICA r[n_, y_] := Reduce[x > 0 && n == x^2 + y^3, x, Integers]; ok[n_] := Catch[Do[If[r[n, y] =!= False, Throw[True]], {y, 1, Ceiling[n^(1/3)]}]] == True; Select[Range[300], ok] (* Jean-François Alcover, Jul 16 2012 *) solQ[n_] := Length[Reduce[p^2 + q^3 == n && p > 0 && q > 0, {p, q}, Integers]] > 0; Select[Range[224], solQ] (* Jayanta Basu, Jul 11 2013 *) PROG (PARI) list(lim)=my(v=List()); for(n=1, sqrtint(lim\1-1), for(m=1, sqrtnint(lim\1-n^2, 3), listput(v, n^2+m^3))); Set(v) \\ Charles R Greathouse IV, May 15 2015 (PARI) is(n)=for(k=1, sqrtnint(n-1, 3), if(issquare(n-k^3), return(1))); 0 \\ Charles R Greathouse IV, May 15 2015 CROSSREFS Cf. A022549, A055393, A078360. Complement of A066650. Sequence in context: A295567 A100530 A155469 * A078360 A114995 A047619 Adjacent sequences:  A055391 A055392 A055393 * A055395 A055396 A055397 KEYWORD easy,nonn AUTHOR Henry Bottomley, May 12 2000 STATUS approved

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Last modified October 22 09:57 EDT 2018. Contains 316433 sequences. (Running on oeis4.)