OFFSET
1,1
COMMENTS
Conjecture: the largest prime in the sequence is 31. (If this is true, then the next terms after 32768 are 49729, 59049, and 65536.)
Every number > 4 that is a power of 2, 3, or 7 is in the sequence.
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.
LINKS
Jon E. Schoenfield, Table of n, a(n) for n = 1..56 (based on b-file for A289631 from Giovanni Resta)
EXAMPLE
5 is not in the sequence because (j^6 + k^6 + m^6) mod 5, where j, k, and m are integers, can take on all 5 values 0..4.
7 is in the sequence because (j^6 + k^6 + m^6) mod 7 can take on only 4 values (0..3), not 7.
14 is not in the sequence because -- although (j^6 + k^6 + m^6) mod 14 can take on only the 8 (not 14) values 0, 1, 2, 3, 7, 8, 9, and 10 -- 14 is not a prime power.
CROSSREFS
KEYWORD
nonn
AUTHOR
Jon E. Schoenfield, Jul 10 2017
EXTENSIONS
a(40)-a(46) added (based on b-file for A289631 from Giovanni Resta) by Jon E. Schoenfield, Jul 15 2017
STATUS
approved