A306586 - OEIS

%I #20 Feb 27 2019 02:52:53

%S 2,5,17,59,223,757,2633,8969,30431,102191,341357,1134043,3749633,

%T 12351797,40558519,132820211,433927019,1414734187,4604123551,

%U 14959716349,48537631577,157280263711,509055969293,1645881130301,5316347779363,17157165731437,55325548493311,178271206357499

%N Least prime p(k) such that k*p exceeds 10^n.

%C The index of the primes of a(n): 1, 3, 7, 17, 48, 134, 382, 1115, 3287, 9786, 29296, 88181, ..., = A090977.

%C a(n)*A090977(n)-10^n, n=0..: 1, 5, 19, 3, 704, 1438, 5806, 435, 26697, 41126, 394672, 1045783, 4623302, ..., .

%H Daniel Suteu, <a href="/A306586/b306586.txt">Table of n, a(n) for n = 0..36</a>

%F a(n) = A000040(A090977(n)).

%e a(0) = 2 since 2*1 > 1 = 10^0;

%e a(1) = 5 since 5*3 = 15 > 10^1;

%e a(2) = 17 since 17*6 = 102 > 10^2;

%e a(3) = 59 since 59*17 = 1003; etc.

%t f[n_] := Block[{k = 1}, While[k*Prime[k] < 10^n, k++]; Prime[k]]; Array[f, 15, 0]

%o (PARI) a(n) = my(i=0); forprime(p=1, , i++; if(i*p > 10^n, return(p))) \\ _Felix Fröhlich_, Feb 26 2019

%Y Cf. A000040, A090977.

%K nonn

%O 0,1

%A _Robert G. Wilson v_, Feb 25 2019