OFFSET
1,2
COMMENTS
The primes do not occur in their natural order, and for all terms studied if a(n) is a prime p, then a(n-1) = p(p-1) and a(n+1) = p(p^2-1). In the first 10000 terms the fixed points are 22, 165, 710, 1005, 9003, although it is likely more exist. The sequence is conjectured to be a permutation of the positive integers.
LINKS
Scott R. Shannon, Table of n, a(n) for n = 1..10000.
EXAMPLE
a(3) = 6 as a(2) + 6 = 2 + 6 = 8 which has 2 as its only distinct prime factor, and 2 is a factor of 6.
a(8) = 42 as a(7) + 42 = 56 + 42 = 96 which has 2 and 3 as distinct prime factors, and 2 and 3 are factors of 42.
a(10) = 336 as a(9) + 336 = 7 + 336 = 343 which has 7 as its only distinct prime factor, and 7 is a factor of 336. Note that 336 = 7(7^2-1).
CROSSREFS
KEYWORD
nonn
AUTHOR
Scott R. Shannon and Eric Angelini, Jan 05 2023
STATUS
approved