A304360 Lexicographically earliest infinite sequence of numbers m > 1 with the property that none of the prime indices of m are in the sequence.

2, 4, 5, 8, 10, 13, 16, 17, 20, 23, 25, 26, 31, 32, 34, 37, 40, 43, 46, 47, 50, 52, 61, 62, 64, 65, 67, 68, 73, 74, 79, 80, 85, 86, 89, 92, 94, 100, 103, 104, 107, 109, 113, 115, 122, 124, 125, 128, 130, 134, 136, 137, 146, 148, 149, 151, 155, 158, 160, 163

Offset

1,1

Comments

A self-describing sequence.

The prime indices of m are the numbers k such that prime(k) divides m.

The sequence is monotonically increasing, since once a number is rejected it stays rejected. Sequence is closed under multiplication for a similar reason. - N. J. A. Sloane, Aug 26 2018

Links

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

Example

After the initial term 2, the next term cannot be 3 because 3 has prime index 2, and 2 is already in the sequence. The next term could be 10, which has prime indices 1 and 3, but 4 (with prime index 1) is smaller. So a(2) = 4.

Maple

A:= NULL:
P:= {}:
for n  from 2 to 1000 do
  pn:= numtheory:-factorset(n);
  if pn intersect P = {} then
    A:= A, n;
    P:= P union {ithprime(n)};
  fi
od:
A; # Robert Israel, Aug 26 2018

Mathematica

gaQ[n_]:=Or[n==0, And@@Cases[FactorInteger[n], {p_, k_}:>!gaQ[PrimePi[p]]]];
Select[Range[100], gaQ]

Crossrefs

Cf. A000002, A001462, A079000, A079254, A214577, A276625, A277098, A280996, A303431.

For first differences see A317963, for primes see A317964.

Sequence in context: A174868 A268381 A186349 * A072437 A115793 A076614

Adjacent sequences: A304357 A304358 A304359 * A304361 A304362 A304363

Keyword

nonn

Author

Gus Wiseman, Aug 16 2018

Extensions

Added "infinite" to definition. - N. J. A. Sloane, Sep 28 2019

Status

approved