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A030665
Smallest nontrivial extension of n which is prime.
10
11, 23, 31, 41, 53, 61, 71, 83, 97, 101, 113, 127, 131, 149, 151, 163, 173, 181, 191, 2003, 211, 223, 233, 241, 251, 263, 271, 281, 293, 307, 311, 3203, 331, 347, 353, 367, 373, 383, 397, 401, 419, 421, 431, 443, 457, 461, 479, 487, 491, 503, 5101
OFFSET
1,1
COMMENTS
The argument in A069695 shows that a(n) always exists. - N. J. A. Sloane, Nov 11 2020
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
EXTENSIONS
Corrected by Ray Chandler, Aug 11 2003
STATUS
approved