A331046 Numbers k such that floor(k/10^m) is a prime number for some m >= 0.

2, 3, 5, 7, 11, 13, 17, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 41, 43, 47, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 61, 67, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 83, 89, 97, 101, 103, 107, 109, 110, 111, 112, 113

Offset: 1

Author

Rémy Sigrist, Jan 08 2020

Keywords

• nonn
• base

Comments

In other words, these are the numbers with a prime prefix.

For any m > 0:

- let f(m) be the proportion of positive numbers <= 10^m belonging to this sequence,

- we have f(m) = Sum_{p < 10^m in A069090} 1/10^A055642(p),

- also f(m) <= f(m+1) <= 1,

- so {f(m)} has a limit, say F, as m tends to infinity,

- what is the value of F?

Examples

			The number 2 is prime, so every number in A217394 belongs to this sequence.
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A055642, A069090, A202259 (complement), A217394, A331044, A331045.

Programs

PARI

is(n,base=10) = while (n, if (isprime(n), return (1), n\=base)); return (0)