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A342962 a(n) is the least prime that starts a string of exactly n distinct primes p_1, p_2, ..., p_n where p_{i+1} = p_i+A085563(p_i), but p_n+A085563(p_n) is either not prime or equal to p_n.

%I A342962 #7 Mar 31 2021 22:39:14
%S A342962 2,29,229,5639,35969,54191353
%N A342962 a(n) is the least prime that starts a string of exactly n distinct primes p_1, p_2, ..., p_n where p_{i+1} = p_i+A085563(p_i), but p_n+A085563(p_n) is either not prime or equal to p_n.
%C A342962 No further terms up to 10^9.
%e A342962 a(3) = 229 because 229, 229+A085563(229) = 233, and 233+A085563(233) = 241 are prime but 241+A085563(241) = 243 is not.
%p A342962 f:= n -> n + convert(select(isprime,convert(n,base,10)),`+`):
%p A342962 F:= proc(n) option remember; local t,x;
%p A342962     x:= f(n);
%p A342962   if x = n or not isprime(x) then 1 else 1+procname(x) fi
%p A342962 end proc:
%p A342962 V:= Vector(6): count:= 0: p:= 1:
%p A342962 while count < 6 do
%p A342962   p:= nextprime(p); v:= F(p);
%p A342962   if v <= 6 and V[v] = 0 then V[v]:= p; count:= count+1 fi
%p A342962 od:
%p A342962 convert(V,list);
%Y A342962 Cf. A085563, A342961.
%K A342962 nonn,base,more
%O A342962 1,1
%A A342962 _J. M. Bergot_ and _Robert Israel_, Mar 31 2021