A331046 - OEIS

%I #12 Jul 24 2021 01:14:15

%S 2,3,5,7,11,13,17,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,

%T 36,37,38,39,41,43,47,50,51,52,53,54,55,56,57,58,59,61,67,70,71,72,73,

%U 74,75,76,77,78,79,83,89,97,101,103,107,109,110,111,112,113

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

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

%C For any m > 0:

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

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

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

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

%C - what is the value of F?

%H Rémy Sigrist, <a href="/A331046/b331046.txt">Table of n, a(n) for n = 1..10000</a>

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

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

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

%K nonn,base

%O 1,1

%A _Rémy Sigrist_, Jan 08 2020