A030665 Smallest nontrivial extension of n which is prime.

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

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.

Index entries for primes involving decimal expansion of n

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

Cf. A018800, A068695, A077501.

Sequence in context: A038904 A179630 A060399 * A077501 A337845 A030675

Adjacent sequences: A030662 A030663 A030664 * A030666 A030667 A030668

Keyword

nonn,base,nice

Author

Patrick De Geest

Extensions

Corrected by Ray Chandler, Aug 11 2003

Status

approved