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%I #39 Nov 11 2020 18:32:28
%S 11,23,31,41,53,61,71,83,97,101,113,127,131,149,151,163,173,181,191,
%T 2003,211,223,233,241,251,263,271,281,293,307,311,3203,331,347,353,
%U 367,373,383,397,401,419,421,431,443,457,461,479,487,491,503,5101
%N Smallest nontrivial extension of n which is prime.
%C The argument in A069695 shows that a(n) always exists. - _N. J. A. Sloane_, Nov 11 2020
%H Chai Wah Wu, <a href="/A030665/b030665.txt">Table of n, a(n) for n = 1..10000</a> [T. D. Noe computed the first 1000 terms]
%H Chai Wah Wu, <a href="http://arxiv.org/abs/1503.08883">On a conjecture regarding primality of numbers constructed from prepending and appending identical digits</a>, arXiv:1503.08883 [math.NT], 2015.
%H <a href="/index/Pri#piden">Index entries for primes involving decimal expansion of n</a>
%e 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.
%e 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.
%p f:= proc(n) local x0, d, r, y;
%p for d from 1 do
%p x0:= n*10^d;
%p for r from 1 to 10^d-1 by 2 do
%p if isprime(x0+r) then
%p return(x0+r)
%p fi
%p od
%p od
%p end proc:
%p seq(f(n), n=1..100); # _Robert Israel_, Dec 23 2014
%t 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 *)
%o (Python)
%o from sympy import nextprime
%o def A030665(n):
%o d, nd = 10, 10*n
%o while True:
%o x = nextprime(nd)
%o if x < nd+d:
%o return int(x)
%o d *= 10
%o nd *= 10 # _Chai Wah Wu_, May 24 2016
%Y Cf. A018800, A068695, A077501.
%K nonn,base,nice
%O 1,1
%A _Patrick De Geest_
%E Corrected by _Ray Chandler_, Aug 11 2003
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