|
| |
|
|
A053000
|
|
a(n) = (smallest prime > n^2) - n^2.
|
|
20
|
|
|
|
2, 1, 1, 2, 1, 4, 1, 4, 3, 2, 1, 6, 5, 4, 1, 2, 1, 4, 7, 6, 1, 2, 3, 12, 1, 6, 1, 4, 3, 12, 7, 6, 7, 2, 7, 4, 1, 4, 3, 2, 1, 12, 13, 12, 13, 2, 13, 4, 5, 10, 3, 8, 3, 10, 1, 12, 1, 2, 7, 10, 7, 6, 3, 20, 3, 4, 1, 4, 13, 22, 3, 10, 5, 4, 1, 14, 3, 10, 5, 6, 21, 2, 9, 10, 1, 4, 15, 4, 9, 6, 1, 6, 3, 14
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
0,1
|
|
|
COMMENTS
|
Suggested by Legendre's conjecture (still open) that there is always a prime between n^2 and (n+1)^2.
Conjecture: a(n) <= 1+phi(n) = 1+A000010(n), for n>0. This improves on Oppermann's conjecture, which says a(n) < n. - Jianglin Luo, Sep 22 2023
|
|
|
REFERENCES
|
J. R. Goldman, The Queen of Mathematics, 1998, p. 82.
|
|
|
LINKS
|
|
|
|
FORMULA
|
|
|
|
MAPLE
|
|
|
|
MATHEMATICA
|
nxt[n_]:=Module[{n2=n^2}, NextPrime[n2]-n2]
|
|
|
PROG
|
(Python)
from sympy import nextprime
def a(n): nn = n*n; return nextprime(nn) - nn
|
|
|
CROSSREFS
|
|
|
|
KEYWORD
|
nonn,easy,nice
|
|
|
AUTHOR
|
|
|
|
EXTENSIONS
|
|
|
|
STATUS
|
approved
|
| |
|
|
