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 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 Paolo P. Lava and T. D. Noe, Table of n, a(n) for n = 1..1000 (first 100 terms from Paolo P. Lava) J. Barkley Rosser and Lowell Schoenfeld, Approximate formulas for some functions of prime numbers, Illinois J. Math. 6 (1962), pp. 64-94. FORMULA a(n) = prime(A085608(n)). - Michel Marcus, Oct 19 2013 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: seq(f(n), n=1..100); # Robert Israel, Dec 23 2014 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 -- Reinhard Zumkeller, Jul 01 2015 (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 print([a(n) for n in range(1, 60)]) # Michael S. Branicky, Nov 02 2021 CROSSREFS Cf. A030665, A068164, A068695, A062584, A088781, A085608. A164022 is the base-2 analog. Cf. also A258337. Row n=1 of A262369. Sequence in context: A077549 A089356 A113616 * A258337 A089566 A010191 Adjacent sequences:  A018797 A018798 A018799 * A018801 A018802 A018803 KEYWORD nonn,base AUTHOR STATUS approved

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Last modified May 20 06:37 EDT 2022. Contains 353852 sequences. (Running on oeis4.)