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A077714 a(1) = 1; thereafter a(n) = the smallest prime of the form d0...0a(n-1), where d is a single digit, or 0 if no such prime exists.

%I A077714 #22 Jun 23 2022 15:42:08
%S A077714 1,11,211,4211,34211,234211,4234211,304234211,9304234211,209304234211,
%T A077714 7209304234211,37209304234211,3037209304234211,23037209304234211,
%U A077714 323037209304234211,70000323037209304234211,300070000323037209304234211,600300070000323037209304234211
%N A077714 a(1) = 1; thereafter a(n) = the smallest prime of the form d0...0a(n-1), where d is a single digit, or 0 if no such prime exists.
%C A077714 a(n) is the smallest prime obtained by prefixing a(n-1) with a number of the form d*10^k where d is a single digit, 0 < d < 10, and k >= 0. Conjecture: d*10^k always exists.
%H A077714 Alois P. Heinz, <a href="/A077714/b077714.txt">Table of n, a(n) for n = 1..52</a>
%e A077714 a(8) = 304234211; deleting 3 gives 4234211 = a(7).
%p A077714 a:= proc(n) option remember; local k, m, d, p;
%p A077714       if n=1 then 1 else k:= a(n-1);
%p A077714         for m from length(k) do
%p A077714           for d to 9 do p:= k +d*10^m;
%p A077714             if isprime(p) then return p fi
%p A077714         od od
%p A077714       fi
%p A077714     end:
%p A077714 seq(a(n), n=1..20);  # _Alois P. Heinz_, Jan 12 2015
%o A077714 (Python)
%o A077714 from sympy import isprime
%o A077714 from itertools import islice
%o A077714 def agen(an=1):
%o A077714     while True:
%o A077714         yield an
%o A077714         pow10 = 10**len(str(an))
%o A077714         while True:
%o A077714             found = False
%o A077714             for t in range(pow10+an, 10*pow10+an, pow10):
%o A077714                 if isprime(t):
%o A077714                     an = t; found = True; break
%o A077714             if found: break
%o A077714             pow10 *= 10
%o A077714 print(list(islice(agen(), 18))) # _Michael S. Branicky_, Jun 23 2022
%Y A077714 Cf. A053582, A077713, A077715, A077716.
%K A077714 base,nonn
%O A077714 1,2
%A A077714 _Amarnath Murthy_, Nov 19 2002
%E A077714 More terms from _Ray Chandler_, Jul 23 2003
%E A077714 Offset changed to 1 by _Alois P. Heinz_, Jan 12 2015
%E A077714 Definition clarified by _N. J. A. Sloane_, Jan 19 2015