A078132 Primes which can be written as sum of cubes > 1.

43, 59, 67, 83, 89, 97, 107, 113, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383

Offset

1,1

Comments

Equivalent to primes which can be written as the sum of cubes of primes; the question being "what is the minimum number of terms in such sums when they can be written in more than one way? - Jonathan Vos Post, Sep 21 2006

Mikawa and Peneva: "One of the famous and still unsettled problems in additive prime number theory is the conjecture that every sufficiently large integer satisfying some natural congruence conditions, can be written as the sum of four cubes of primes. Although the present methods lack the power to prove such a strong result, Hua... has been able to prove that every sufficiently large odd integer as the sum of nine cubes of primes. He also established that almost all integers {n == 1 mod 2, n =/= 0, +/-2 mod 9, n =/= 0 mod 7} can be expressed as the sum of five cubes of primes." - Jonathan Vos Post, Sep 21 2006

Links

Table of n, a(n) for n=1..53.

Eric Weisstein's World of Mathematics, Cubic Number.

Index entries for sequences related to sums of cubes

Hiroshi Mikawa and Temenoujka Peneva, Sums of Five Cubes of Primes in Short Intervals.

Example

A000040(25) = 97 = 3^3 + 3^3 + 3^3 + 2^3 + 2^3, therefore 97 is a term.

Crossrefs

Cf. A000578, A078128, A078133, A000040, A078138.

Primes in A122612.

Sequence in context: A180546 A166491 A127880 * A201613 A115404 A033223

Adjacent sequences: A078129 A078130 A078131 * A078133 A078134 A078135

Keyword

nonn

Author

Reinhard Zumkeller, Nov 19 2002

Status

approved