

A331046


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


1



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
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OFFSET

1,1


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?


LINKS

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


EXAMPLE

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


PROG

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


CROSSREFS

Cf. A055642, A069090, A202259 (complement), A217394, A331044, A331045.
Sequence in context: A242120 A259277 A152073 * A329150 A230606 A117289
Adjacent sequences: A331043 A331044 A331045 * A331047 A331048 A331049


KEYWORD

nonn,base,changed


AUTHOR

Rémy Sigrist, Jan 08 2020


STATUS

approved



