OFFSET
0,1
COMMENTS
If n is an even positive exponent, then a(n) is the first prime greater than 10^(n/2) squared less 10^n.
LINKS
Chai Wah Wu, Table of n, a(n) for n = 0..42
Dario Alejandro Alpern, Brilliant numbers
MATHEMATICA
NextPrim[n_] := Block[{k = n + 1}, While[ !PrimeQ[k], k++ ]; k]; LengthBase10[n_] := Floor[ Log[10, n] + 1]; f[n_] := Block[{k = 0}, If[ EvenQ[n] && n > 1, NextPrim[ 10^(n/2)]^2 - 10^n, While[fi = FactorInteger[10^n + k]; Plus @@ Flatten[ Table[ # [[2]], {1}] & /@ fi] != 2 || Length[ Union[ LengthBase10 /@ Flatten[ Table[ # [[1]], {1}] & /@ fi]]] != 1, k++ ]; k]]; Table[ f[n], {n, 0, 30}]
PROG
(Python)
from sympy import nextprime, factorint
def A083289(n):
a, b = divmod(n, 2)
c, d = 10**n, 10**a
if b == 0: return nextprime(d)**2-c
k = 0
while True:
fs = factorint(c+k, multiple=True)
if len(fs) == 2 and min(fs) >= d:
return k
k += 1 # Chai Wah Wu, Sep 28 2021
CROSSREFS
KEYWORD
base,nonn
AUTHOR
Jason Earls, Jun 03 2003
EXTENSIONS
Edited and extended by Robert G. Wilson v, Jun 27 2003
STATUS
approved