A176649 Primes p = k^13 + m^13 + n^13 with nonnegative integer bases k, m, n.

2, 3, 135812051, 1223891771, 1287820181, 2441406251, 13062296531, 96890604731, 2541865828331, 10000068703187, 34535772846139, 34620821857463, 69142313298269, 106993206981587, 106994426090389, 107007486776213

Offset

1,1

Comments

Necessarily (I) two bases are even and one is odd or (II) all bases are odd.

2 = 1^13 + 1^13 is the only 2-item term of sequence because with an odd exponent e a^e + b^e has the divisor a+b.

List of (k,m,n): (0,1,1) (1,1,1) (3,4,4) (3,3,5) (2,4,5) (1,5,5) (2,3,6) (1,3,7) (1,1,9) (3,4,10) (2,6,11) (5,7,11) (7,11,11) (2,3,12) (2,5,12) (5,6,12) (4,6,13) (8,8,13) (4,12,13) (4,11,14) (6,11,14) (5,12,14) (11,12,14) (3,14,14) (2,2,15) (1,3,15) (2,6,15) (14,14,15) (7,15,15) (1,6,16) (2,13,16) (2,4,17) (3,9,17) (5,9,17) (1,11,17) (2,12,17) (6,14,17) (11,12,18) (10,13,18) (14,15,18) (11,18,18) (1,3,19) (4,8,19) (3,9,19) (7,11,19) (14,14,19) (3,15,19) (7,15,19) (12,15,20) (11,16,20)

Links

Table of n, a(n) for n=1..16.

Example

3^13 + 3^13 + 4^13 = 135812051 = prime(7688710), 3rd term.
3^13 + 3^13 + 5^13 = 1223891771 = prime(61596945), 4th term, smallest with 3 prime bases.
5^13 + 7^13 + 11^13 = 34620821857463, 12th term, the smallest with 3 different prime bases.

Crossrefs

Cf. A000040, A001022.

Sequence in context: A120313 A216981 A307255 * A216979 A334822 A082871

Adjacent sequences: A176646 A176647 A176648 * A176650 A176651 A176652

Keyword

nonn

Author

Eva-Maria Zschorn (e-m.zschorn(AT)zaschendorf.km3.de), Apr 22 2010

Status

approved