OFFSET
1,2
COMMENTS
For (k+1)^3 similar sequence is finite {1, 2, 3, 5, 9, 11, 14}, while for (k+1)^2 it is just {1, 2, 3, 5}. Starting with power 4 (this sequence), the number of values of k is infinite. One series of values for power 6 is given by A001570.
Formed by the union of 10 linear recurrent sequences satisfying b(n) = q*b(n-1) - b(n-2) - 4: A350919 (q=3), A350920 (q=4), A350921 (q=6), A350922 (q=7), A350923 (q=10), A103974 (q=14), A350924 (q=16), A350925 (q=16), A350926 (q=23), A350917 (q=23). Each of them give identities (b(n)+1)^4 = (b(n)*b(n-1)-1) * (b(n)*b(n+1)-1).
Only terms 1, 2, 5, 9, 11, 14, 29 are shared between two or more sequences, all others come from exactly one sequence.
LINKS
Max Alekseyev, Table of n, a(n) for n = 1..5000
PROG
(PARI) { for(k=1, 10^6, fordiv((k+1)^4, d, if(Mod(d, k)==-1, print1(k, ", "); break)) ); }
CROSSREFS
KEYWORD
nonn
AUTHOR
Max Alekseyev, Jan 21 2022
STATUS
approved