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A338715 Smallest prime ending with decimal expansion of n, for n relatively prime to 10.

%I A338715 #26 Jul 09 2025 04:54:27
%S A338715 11,3,7,19,11,13,17,19,421,23,127,29,31,233,37,139,41,43,47,149,151,
%T A338715 53,157,59,61,163,67,269,71,73,277,79,181,83,487,89,191,193,97,199,
%U A338715 101,103,107,109,2111,113,1117,3119,3121,1123,127,1129,131,4133,137,139,2141,2143,5147,149,151,1153,157
%N A338715 Smallest prime ending with decimal expansion of n, for n relatively prime to 10.
%C A338715 a(n) exists by Dirichlet's theorem.
%H A338715 Robert Israel, <a href="/A338715/b338715.txt">Table of n, a(n) for n = 1..10000</a>
%H A338715 <a href="/index/Pri#piden">Index entries for primes involving decimal expansion of n</a>
%p A338715 N:= 100: # for a(1) to a(N)
%p A338715 V:= Vector(N):
%p A338715 count:= 0:
%p A338715 for n from 1 while count < N do
%p A338715   if igcd(n,10)=1 then
%p A338715     count:= count+1;
%p A338715     d:= ilog10(n)+1;
%p A338715     for x from n by 10^d do
%p A338715       if isprime(x) then V[count]:= x; break fi
%p A338715     od
%p A338715   fi
%p A338715 od:
%p A338715 convert(V,list); # _Robert Israel_, Nov 11 2020
%o A338715 (Python)
%o A338715 from sympy import isprime
%o A338715 def a(n):
%o A338715     ending = 2*n - 1 + (n+1)//4 * 2 # A045572
%o A338715     i, pow10 = ending, 10**len(str(ending))
%o A338715     while not isprime(i): i += pow10
%o A338715     return i
%o A338715 print([a(n) for n in range(1, 64)]) # _Michael S. Branicky_, Nov 03 2021
%Y A338715 Cf. A045572, A105888 (base 2 equivalent), A258190.
%Y A338715 See A245193, A337834, A338716 for other versions.
%K A338715 nonn,base,look
%O A338715 1,1
%A A338715 _N. J. A. Sloane_, Nov 11 2020
%E A338715 More terms from _Robert Israel_, Nov 11 2020