login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A138854 Numbers which are the sum of three cubes of distinct primes. 6
160, 378, 476, 495, 1366, 1464, 1483, 1682, 1701, 1799, 2232, 2330, 2349, 2548, 2567, 2665, 3536, 3555, 3653, 3871, 4948, 5046, 5065, 5264, 5283, 5381, 6252, 6271, 6369, 6587, 6894, 6992, 7011, 7118, 7137, 7210, 7229, 7235, 7327, 7453, 8198, 8217, 8315 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

This is a subset of A024975. The odd terms of this sequence are A138853, the even terms are 8+{ even terms of A120398 }. Thus primes in this sequence, A137365, are the same than primes in A138853.

LINKS

Chai Wah Wu, Table of n, a(n) for n = 1..10000 (terms 1..621 from R. J. Mathar)

Index to sequences related to sums of cubes.

FORMULA

A138854 = { p(i)^3+p(j)^3+p(k)^3 ; i>j>k>0 } = A138853 union { p(i)^3+p(j)^3+8 ; i>j>1}

MAPLE

isA030078 := proc(n)

    local f ;

    if n < 8 then

        false;

    else

        f := ifactors(n)[2] ;

        if nops(f) = 1 and op(2, op(1, f)) = 3 then

            true;

        else

            false;

        end if;

    end if;

end proc:

isA138854 := proc(n)

    local i, j, p, q, r, rcub ;

    for i from 1 do

        p := ithprime(i) ;

        if p^3+(p+1)^3+(p+2)^3 > n then

            return false;

        end if;

        for j from i+1 do

            q := ithprime(j) ;

            rcub := n-q^3-p^3 ;

            if rcub <= q^3 then

                break;

            fi ;

            if isA030078(rcub) then

                return true;

            end if;

        end do:

    end do:

end proc:

for n from 5 do

    if isA138854(n) then

        print(n);

    end if;

end do: # R. J. Mathar, Jun 09 2014

MATHEMATICA

f[upto_]:=Module[{maxp=PrimePi[Floor[Power[upto, (3)^-1]]]}, Select[Union[Total/@(Subsets[Prime[Range[maxp]], {3}]^3)], #<=upto&]]; f[9000]  (* Harvey P. Dale, Mar 21 2011 *)

PROG

(PARI) isA138854(n)={ if( n%2, isA138853(n), isA120398(n-8)) }

for( n=1, 10^4, isA138854(n) & print1(n", "))

CROSSREFS

Cf. A024975 (a^3+b^3+c^3, a>b>c>0), A138853 (odd terms of this), A120398, A137365 (primes in A138853 / A138854).

Sequence in context: A060675 A171225 A127338 * A133530 A278129 A184070

Adjacent sequences:  A138851 A138852 A138853 * A138855 A138856 A138857

KEYWORD

nonn

AUTHOR

M. F. Hasler, Apr 13 2008

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified July 23 22:27 EDT 2017. Contains 289716 sequences.