A003999 Sums of distinct nonzero 4th powers.

1, 16, 17, 81, 82, 97, 98, 256, 257, 272, 273, 337, 338, 353, 354, 625, 626, 641, 642, 706, 707, 722, 723, 881, 882, 897, 898, 962, 963, 978, 979, 1296, 1297, 1312, 1313, 1377, 1378, 1393, 1394, 1552, 1553, 1568, 1569, 1633, 1634, 1649, 1650, 1921, 1922

Offset

1,2

Comments

5134240 is the largest positive integer not in this sequence. - Jud McCranie

If we tightened the sequence requirement so that the sum was of more than one 4th power, we would remove exactly 32 4th powers from the terms: row 4 of A332065 indicates which 4th powers would remain. After a(1) = 1, the next number in this sequence that is in the analogous sequences for cubes and squares is a(24) = 881 = A364637(4). - Peter Munn, Aug 01 2023

References

The Penguin Dictionary of Curious and Interesting Numbers, David Wells, entry 5134240.

Links

Donovan Johnson, Table of n, a(n) for n = 1..10000

Index entries for linear recurrences with constant coefficients, signature (2,-1).

Formula

For n > 4244664, a(n) = n + 889576. - Charles R Greathouse IV, Sep 02 2011

Maple

(1+x)*(1+x^16)*(1+x^81)*(1+x^256)*(1+x^625)*(1+x^1296)*(1+x^2401)*(1+x^4096)*(1+x^6561)*(1+x^10000)

Mathematica

max = 2000; f[x_] := Product[1 + x^(k^4), {k, 1, 10}]; Exponent[#, x]& /@ List @@ Normal[Series[f[x], {x, 0, max}]] // Rest (* Jean-François Alcover, Nov 09 2012, after Charles R Greathouse IV *)

Prog

(PARI) upto(lim)={
    lim\=1;
    my(v=List(), P=prod(n=1, lim^(1/4), 1+x^(n^4), 1+O(x^(lim+1))));
    for(n=1, lim, if(polcoeff(P, n), listput(v, n)));
    Vec(v)
}; \\ Charles R Greathouse IV, Sep 02 2011

Crossrefs

Cf. A046039 (complement).

Cf. A003995, A003997, A194768, A194769 (analogs for squares, cubes, 5th and 6th powers).

Cf. A001661, A332065, A364637.

A217844 is a subsequence.

Sequence in context: A041530 A041528 A112012 * A217844 A041532 A341114

Adjacent sequences: A003996 A003997 A003998 * A004000 A004001 A004002

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved