OFFSET
1,1
COMMENTS
Every number > 3 that is a power of 2, 3, or 7 is in the sequence.
Primes in this sequence begin 7, 13, 19, 31, 37, 43, 61, 67, 73, 79, 109, 139, 223.
Conjecture: 223 is the final prime in this sequence.
From Jon E. Schoenfield, Jul 14 2017: (Start)
If any prime power P = p^k (where p is prime and k >= 1) is in the sequence, then so is p^j for all j > k.
Conjecture: the terms in this sequence that are the squares of primes are the squares of 13, 37, 61, 73, 109, and every prime not congruent to 1 mod 4.
(End)
LINKS
Giovanni Resta, Table of n, a(n) for n = 1..192 (terms < 2*10^6)
EXAMPLE
PROG
(PARI) isok(n) = isprimepower(n) && (#Set(vector(n^2, i, ((i%n)^6 + (i\n)^6) % n)) < n); \\ Michel Marcus, Jul 11 2017
CROSSREFS
Cf. A289740 (similar sequence for sums of three sixth powers), A289760 (similar sequence for sums of four sixth powers). - Jon E. Schoenfield, Jul 14 2017
KEYWORD
nonn
AUTHOR
Jon E. Schoenfield, Jul 08 2017
STATUS
approved