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A048552 a(n+1) is next smallest prime beginning with a(n), initial prime is a(0) = 7.

%I A048552 #17 Jan 28 2020 01:22:31
%S A048552 7,71,719,7193,71933,719333,71933317,719333177,71933317711,
%T A048552 7193331771103,71933317711039,7193331771103939,719333177110393913,
%U A048552 7193331771103939133,719333177110393913323,71933317711039391332309,719333177110393913323097,719333177110393913323097047
%N A048552 a(n+1) is next smallest prime beginning with a(n), initial prime is a(0) = 7.
%H A048552 Robert Israel, <a href="/A048552/b048552.txt">Table of n, a(n) for n = 0..250</a>
%p A048552 f:= proc(n) option remember; local q,d,v;
%p A048552     q:=procname(n-1);
%p A048552     for d from 1 do
%p A048552       v:= nextprime(q*10^d);
%p A048552       if v < (q+1)*10^d then return v fi
%p A048552     od
%p A048552 end proc:
%p A048552 f(0):= 7:
%p A048552 map(f, [$0..20]); # _Robert Israel_, Jan 26 2020
%t A048552 Nest[Function[{a, n}, Append[#, Catch@ Do[Do[If[PrimeQ@ #, Throw@ #; Break[], #] &@ FromDigits[n~Join~PadLeft[IntegerDigits[(5 j - 4 + Mod[3 j + 2, 4])/2], i]], {j, 4*10^(i - 1)}], {i, Infinity}]]] @@ {#, IntegerDigits[#[[-1]] ]} &, {7}, 17] (* _Michael De Vlieger_, Jan 26 2020 *)
%o A048552 (PARI)
%o A048552 next_A048552(p)=for(i=1,oo,my(q=nextprime(p*=10));q-p>10^i||return(q))
%o A048552 A048552(n,p=7)=vector(n,i,i>1&&p=next_A048552(p);p) \\ _M. F. Hasler_, Jan 26 2020
%Y A048552 Cf. A048549, A048550, A048551, A048552, A048553, A048554, A048555, A048556.
%K A048552 nonn,base
%O A048552 0,1
%A A048552 _Patrick De Geest_, May 15 1999