OFFSET
1,1
COMMENTS
Up to prime 669763117 all gaps are 8 and 64 or 64 and 8. Prime 669763117 is the first one with gaps 8 and 216. Possible gaps must be in A016743.
LINKS
Karl-Heinz Hofmann, Table of n, a(n) for n = 1..10000
EXAMPLE
a(2) = 107441; previous prime is 107377 and the gap is 64 (a cube); next prime is 107449 and the gap is 8 (a cube too).
MAPLE
iscube:= proc(n) option remember; is(n=iroot(n, 3)^3) end:
q:= n-> isprime(n) and andmap(iscube, [n-prevprime(n), nextprime(n)-n]):
select(q, [$3..3500000])[]; # Alois P. Heinz, Apr 25 2022
MATHEMATICA
p = Prime[Range[3*10^5]]; pos = Position[Differences[p], _?(IntegerQ@Surd[#, 3] &)] // Flatten; p[[pos[[Position[Differences[pos], 1] // Flatten]] + 1]] (* Amiram Eldar, Apr 26 2022 *)
PROG
CROSSREFS
Cf. A353136 (triangular numbers gaps).
KEYWORD
nonn
AUTHOR
Karl-Heinz Hofmann, Apr 25 2022
STATUS
approved