|
|
A018800
|
|
Smallest prime that begins with n.
|
|
16
|
|
|
11, 2, 3, 41, 5, 61, 7, 83, 97, 101, 11, 127, 13, 149, 151, 163, 17, 181, 19, 2003, 211, 223, 23, 241, 251, 263, 271, 281, 29, 307, 31, 3203, 331, 347, 353, 367, 37, 383, 397, 401, 41, 421, 43, 443, 457, 461, 47, 487, 491, 503, 5101, 521, 53, 541, 557, 563, 571, 587, 59
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
Conjecture: If a(n) = (n concatenated with k) then k < n. - Amarnath Murthy, May 01 2002
a(n) always exists. Proof. Suppose n is L digits long, and consider the numbers between n*10^B and n*10^B+10^C, where B > C are both large compared with L. All such numbers begin with the digits of n. Using the upper and lower bounds on pi(x) from Theorem 1 of Rosser and Schoenfeld, it follows that for sufficiently large B and C, at least one of these numbers is a prime. QED - N. J. A. Sloane, Nov 14 2014
|
|
LINKS
|
|
|
FORMULA
|
|
|
MAPLE
|
f:= proc(n) local x0, d, r, y;
if isprime(n) then return(n) fi;
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:
|
|
MATHEMATICA
|
Table[Function[d, FromDigits@ SelectFirst[ IntegerDigits@ Prime@ Range[10^4], Length@ # >= Length@ d && Take[#, Length@ d] == d &]][ IntegerDigits@ n], {n, 59}] (* Michael De Vlieger, May 24 2016, Version 10 *)
|
|
PROG
|
(Haskell)
import Data.List (isPrefixOf, find); import Data.Maybe (fromJust)
a018800 n = read $ fromJust $
find (show n `isPrefixOf`) $ map show a000040_list :: Int
(PARI) a(n{, base=10}) = for (l=0, oo, forprime (p=n*base^l, (n+1)*base^l-1, return (p))) \\ Rémy Sigrist, Jun 11 2017
(Python)
from sympy import isprime
def a(n):
if isprime(n): return n
pow10 = 10
while True:
t, maxt = n * pow10 + 1, (n+1) * pow10
while t < maxt:
if isprime(t): return t
t += 2
pow10 *= 10
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,base
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|