A320629 - OEIS (original) (raw)

1, 7, 13, 19, 23, 29, 37, 43, 47, 49, 53, 61, 71, 73, 79, 89, 91, 97, 101, 103, 107, 113, 131, 133, 137, 139, 149, 151, 161, 163, 167, 169, 173, 181, 193, 197, 199, 203, 223, 227, 229, 233, 239, 247, 251, 257, 259, 263, 269, 271, 281, 293, 299, 301, 307, 311

COMMENTS

The index of a prime number n is the number m such that n is the m-th prime.

The asymptotic density of this sequence is (1/2) * Product_{p in A006450} (1 - 1/p) = 1/(2*Sum_{n>=1} 1/A076610(n)) < 1/6. - Amiram Eldar, Feb 02 2021

EXAMPLE

The sequence of terms begins:

1 = 1

7 = prime(4)

13 = prime(6)

19 = prime(8)

23 = prime(9)

29 = prime(10)

37 = prime(12)

43 = prime(14)

47 = prime(15)

49 = prime(4)^2

53 = prime(16)

61 = prime(18)

71 = prime(20)

73 = prime(21)

79 = prime(22)

89 = prime(24)

91 = prime(4)*prime(6)

97 = prime(25)

101 = prime(26)

103 = prime(27)

107 = prime(28)

113 = prime(30)

131 = prime(32)

133 = prime(4)*prime(8)

137 = prime(33)

139 = prime(34)

149 = prime(35)

151 = prime(36)

161 = prime(4)*prime(9)

MATHEMATICA

Select[Range[1, 100, 2], And@@Not/@PrimeQ/@PrimePi/@First/@FactorInteger[#]&]

CROSSREFS

Cf. A000040, A006450, A007821, A018252, A056239, A076610, A112798, A302242, A320533, A320628, A320630, A320631, A320633.