A344948 - OEIS

A344948

Primes whose position among the powers of primes (A000961) is also prime.

%I #11 Jun 06 2021 10:25:38

%S 2,3,5,19,29,47,67,73,101,113,137,167,193,199,239,263,313,349,389,419,

%T 431,449,461,487,571,599,641,701,719,751,797,823,857,887,911,977,991,

%U 1019,1097,1193,1223,1231,1277,1301,1307,1399,1439,1481,1511,1531,1571,1601

%N Primes whose position among the powers of primes (A000961) is also prime.

%H Michel Marcus, <a href="/A344948/b344948.txt">Table of n, a(n) for n = 1..10000</a>

%e The position of 2 in A000961 is 2; so 2 is a term.

%e The position of 19 in A000961 is 13; so 19 is a term.

%t pow = Select[Range[1600], # == 1 || PrimePowerQ[#] &]; Select[pow[[Select[Range @ Length[pow], PrimeQ]]], PrimeQ] (* _Amiram Eldar_, Jun 03 2021 *)

%o (PARI) allmps(nn) = {my(map = Map()); mapput(map, 1, 1); my(nb=1); for (n=2, nn, if (isprimepower(n), nb++; mapput(map, n, nb));); map;}

%o lista(nn) = {my(nb = prime(nn), map = allmps(nb)); forprime (p=1, nn, if( isprime(mapget(map, p)), print1(p, ", ")););}

%Y Cf. A000040, A000961, A024620.

%K nonn

%O 1,1

%A _Michel Marcus_, Jun 03 2021