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

2, 11, 107, 191, 587, 719, 1061, 1171, 1181, 1259, 1327, 1487, 1597, 1619, 1933, 1949, 2011, 2141, 2269, 2477, 2803, 2999, 3041, 3049, 3079, 3169, 3229, 3259, 3617, 3733, 4493, 4799, 5009, 5023, 5171, 5261, 5581, 5657, 6131, 6211, 6301, 6311, 6421, 6451, 6529

Offset: 1

Author

Peter Weiss, Sep 19 2017

Keywords

• nonn
• base

Comments

If p is in the sequence, its index A000720(p) is not divisible by 3. - Robert Israel, Sep 19 2017

Examples

			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.
		

Crossrefs

Cf. A000720, A062028, A007618, A004207.

Programs

Maple

f:= proc(n) local t, p;
  p:= ithprime(n);
  t:= n;
  do
    t:= t + convert(convert(t,base,10),`+`);
    if t > p then return NULL
    elif t = p then return p
    fi
  od;
end proc:
map(f, [$1..1000]); # Robert Israel, Sep 19 2017

Mathematica

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 *)

PARI

is(n) = my(x=primepi(n)); while(1, x=x+sumdigits(x); if(x==n, return(1), if(x > n, return(0))))
forprime(p=1, 7000, if(is(p), print1(p, ", "))) \\ Felix Fröhlich, Sep 19 2017

Extensions

More terms from Felix Fröhlich, Sep 19 2017