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A292566 Primes that can be reached with their prime-index, if you start with the prime-index and use iterations of A062028.

%I A292566 #11 Sep 21 2017 17:00:44
%S A292566 2,11,107,191,587,719,1061,1171,1181,1259,1327,1487,1597,1619,1933,
%T A292566 1949,2011,2141,2269,2477,2803,2999,3041,3049,3079,3169,3229,3259,
%U A292566 3617,3733,4493,4799,5009,5023,5171,5261,5581,5657,6131,6211,6301,6311,6421,6451,6529
%N A292566 Primes that can be reached with their prime-index, if you start with the prime-index and use iterations of A062028.
%C A292566 If p is in the sequence, its index A000720(p) is not divisible by 3. - _Robert Israel_, Sep 19 2017
%e A292566 The prime-index of 11 is 5: 5+5=10, 10+1+0=11 -> after two iterations you reach 11, so 11 is in the sequence.
%p A292566 f:= proc(n) local t, p;
%p A292566   p:= ithprime(n);
%p A292566   t:= n;
%p A292566   do
%p A292566     t:= t + convert(convert(t,base,10),`+`);
%p A292566     if t > p then return NULL
%p A292566     elif t = p then return p
%p A292566     fi
%p A292566   od;
%p A292566 end proc:
%p A292566 map(f, [$1..1000]); # _Robert Israel_, Sep 19 2017
%t A292566 ok[p_] := Block[{n = PrimePi@ p}, While [n < p, n += Total@ IntegerDigits@ n]; n == p]; Select[Prime@ Range@ 600, ok] (* _Giovanni Resta_, Sep 19 2017 *)
%o A292566 (PARI) is(n) = my(x=primepi(n)); while(1, x=x+sumdigits(x); if(x==n, return(1), if(x > n, return(0))))
%o A292566 forprime(p=1, 7000, if(is(p), print1(p, ", "))) \\ _Felix Fröhlich_, Sep 19 2017
%Y A292566 Cf. A000720, A062028, A007618, A004207.
%K A292566 nonn,base
%O A292566 1,1
%A A292566 _Peter Weiss_, Sep 19 2017
%E A292566 More terms from _Felix Fröhlich_, Sep 19 2017