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A342958 a(n) is the least prime that starts a string of exactly n primes p_1, p_2, ... p_n where p_{i+1} = p_i-A003132(p_i), but p_n-A003132(p_n) is not prime.

%I A342958 #4 Mar 31 2021 20:24:44
%S A342958 2,13,547,10559,246349,20020109,20020163
%N A342958 a(n) is the least prime that starts a string of exactly n primes p_1, p_2, ... p_n where p_{i+1} = p_i-A003132(p_i), but p_n-A003132(p_n) is not prime.
%C A342958 No further terms < 10^9.
%e A342958 a(3) = 547 because 547, 547-A003132(547) = 457, and 457-A003132(457) = 367 are prime, but 367-A003132(367) = 273 is not prime.
%p A342958 f:= proc(n) option remember; local t, x;
%p A342958   x:= n - add(t^2, t=convert(n, base, 10));
%p A342958   if not isprime(x) then 1 else 1+procname(x) fi
%p A342958 end proc:
%p A342958 V:= Vector(7): count:= 0: p:= 1:
%p A342958 while count < 7 do
%p A342958   p:= nextprime(p); v:= f(p);
%p A342958   if v <= N and V[v] = 0 then V[v]:= p; count:= count+1 fi
%p A342958 od:
%p A342958 convert(V, list);
%Y A342958 Cf. A003132, A179549, A342953.
%K A342958 nonn,more,base
%O A342958 1,1
%A A342958 _J. M. Bergot_ and _Robert Israel_, Mar 31 2021