OFFSET
1,1
COMMENTS
The argument in A069695 shows that a(n) always exists. - N. J. A. Sloane, Nov 11 2020
LINKS
Chai Wah Wu, Table of n, a(n) for n = 1..10000 [T. D. Noe computed the first 1000 terms]
Chai Wah Wu, On a conjecture regarding primality of numbers constructed from prepending and appending identical digits, arXiv:1503.08883 [math.NT], 2015.
EXAMPLE
For n = 1, we could append 1, 3, 7, 9, 01, etc., to make a prime, but 1 gives the smallest of these, 11, so a(1) = 11.
For n = 2, although 2 is already prime, the definition requires an appending at least one digit. 1 doesn't work because 21 = 3 * 7, but 3 does because 23 is prime. Hence a(2) = 23.
MAPLE
f:= proc(n) local x0, d, r, y;
for d from 1 do
x0:= n*10^d;
for r from 1 to 10^d-1 by 2 do
if isprime(x0+r) then
return(x0+r)
fi
od
od
end proc:
seq(f(n), n=1..100); # Robert Israel, Dec 23 2014
MATHEMATICA
A030665[n_] := Module[{d = 10, nd = 10 * n}, While[True, x = NextPrime[nd]; If[x < nd + d, Return[x]]; d *= 10; nd *= 10]]; Array[A030665, 100] (* Jean-François Alcover, Oct 19 2016, translated from Chai Wah Wu's Python code *)
PROG
(Python)
from sympy import nextprime
def A030665(n):
d, nd = 10, 10*n
while True:
x = nextprime(nd)
if x < nd+d:
return int(x)
d *= 10
nd *= 10 # Chai Wah Wu, May 24 2016
CROSSREFS
KEYWORD
nonn,base,nice
AUTHOR
EXTENSIONS
Corrected by Ray Chandler, Aug 11 2003
STATUS
approved