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A077715 a(1) = 7; 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 A077715 #19 Jun 23 2022 15:42:12
%S A077715 7,17,317,6317,26317,126317,2126317,72126317,372126317,5372126317,
%T A077715 305372126317,9305372126317,409305372126317,20409305372126317,
%U A077715 100020409305372126317,9100020409305372126317,209100020409305372126317,40209100020409305372126317
%N A077715 a(1) = 7; 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 A077715 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 A077715 Michael S. Branicky, <a href="/A077715/b077715.txt">Table of n, a(n) for n = 1..50</a>
%p A077715 a:= proc(n) option remember; local k, m, d, p;
%p A077715       if n=1 then 7 else k:= a(n-1);
%p A077715         for m from length(k) do
%p A077715           for d to 9 do p:= k +d*10^m;
%p A077715             if isprime(p) then return p fi
%p A077715         od od
%p A077715       fi
%p A077715     end:
%p A077715 seq(a(n), n=1..20);  # _Alois P. Heinz_, Jan 12 2015
%o A077715 (Python)
%o A077715 from sympy import isprime
%o A077715 from itertools import islice
%o A077715 def agen(an=7):
%o A077715     while True:
%o A077715         yield an
%o A077715         pow10 = 10**len(str(an))
%o A077715         while True:
%o A077715             found = False
%o A077715             for t in range(pow10+an, 10*pow10+an, pow10):
%o A077715                 if isprime(t):
%o A077715                     an = t; found = True; break
%o A077715             if found: break
%o A077715             pow10 *= 10
%o A077715 print(list(islice(agen(), 18))) # _Michael S. Branicky_, Jun 23 2022
%Y A077715 Cf. A053584, A077713, A077714, A077716.
%K A077715 base,nonn
%O A077715 1,1
%A A077715 _Amarnath Murthy_, Nov 19 2002
%E A077715 More terms from _Ray Chandler_, Jul 23 2003
%E A077715 Definition clarified by _N. J. A. Sloane_, Jan 19 2015