A324695 - OEIS

A324695

Lexicographically earliest sequence of positive integers whose prime indices are not already in the sequence.

1, 3, 7, 9, 11, 13, 19, 21, 27, 29, 33, 37, 39, 43, 47, 49, 53, 57, 59, 61, 63, 71, 77, 79, 81, 83, 87, 89, 91, 97, 99, 101, 107, 111, 113, 117, 121, 127, 129, 131, 133, 139, 141, 143, 147, 149, 151, 159, 163, 169, 171, 173, 177, 179, 181, 183, 189, 193, 197

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OFFSET

1,2

COMMENTS

A self-describing sequence, similar to A304360.

A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798.

LINKS

Table of n, a(n) for n=1..59.

EXAMPLE

The sequence of terms together with their prime indices begins:

1: {}

3: {2}

7: {4}

9: {2,2}

11: {5}

13: {6}

19: {8}

21: {2,4}

27: {2,2,2}

29: {10}

33: {2,5}

37: {12}

39: {2,6}

43: {14}

47: {15}

49: {4,4}

53: {16}

57: {2,8}

59: {17}

61: {18}

63: {2,2,4}

MATHEMATICA

aQ[n_]:=And@@Cases[If[n==1, {}, FactorInteger[n]], {p_, k_}:>!aQ[PrimePi[p]]];

Select[Range[100], aQ]

CROSSREFS

Complement of A324694. Prime indices are A304360.

Cf. A000002, A000720, A001222, A001462, A007097, A055396, A061395, A079000, A079254, A109298, A112798, A276625, A277098.

Cf. A324696, A324697, A324698, A324699, A324700, A324701, A324702, A324703, A324704, A324705.

Sequence in context: A104381 A136333 A134454 * A113522 A222262 A027897

Adjacent sequences: A324692 A324693 A324694 * A324696 A324697 A324698

KEYWORD

nonn

AUTHOR

Gus Wiseman, Mar 10 2019

STATUS

approved