A317964 Prime numbers in the lexicographically earliest sequence of positive integers whose prime indices are not already in the sequence (A304360).

2, 5, 13, 17, 23, 31, 37, 43, 47, 61, 67, 73, 79, 89, 103, 107, 109, 113, 137, 149, 151, 163, 167, 179, 181, 193, 197, 223, 227, 233, 241, 251, 257, 263, 269, 271, 277, 281, 307, 317, 347, 349, 353, 359, 379, 383, 389, 397, 419, 421, 431, 433, 449, 457, 463, 467, 487, 499, 503, 509, 521, 523, 547

Offset

1,1

Comments

Also primes whose prime index is not in A304360, or is in A324696. A prime index of n is a number m such that prime(m) divides n. - Gus Wiseman, Mar 19 2019

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Maple

count:= 0:
P:= {}: A:= NULL:
for n from 2 while count < 100 do
  pn:= numtheory:-factorset(n);
  if pn intersect P = {} then
    P:= P union {ithprime(n)};
    if isprime(n) then A:= A, n; count:= count+1 fi;
  fi
od:
A; # Robert Israel, Aug 26 2018

Mathematica

aQ[n_]:=n==1||Or@@Cases[FactorInteger[n], {p_, _}:>!aQ[PrimePi[p]]];
Prime[Select[Range[100], aQ]] (* Gus Wiseman, Mar 19 2019 *)

Crossrefs

Cf. A000720, A001462, A007097, A060197, A079254, A112798, A276625, A277098, A290822, A304360, A306844.

Cf. A324695, A324698, A324704, A324741, A324756, A324758, A324765, A324766, A324768.

Sequence in context: A215424 A215428 A019362 * A075451 A109515 A135933

Adjacent sequences: A317961 A317962 A317963 * A317965 A317966 A317967

Keyword

nonn

Author

N. J. A. Sloane, Aug 26 2018

Status

approved