A306586 Least prime p(k) such that k*p exceeds 10^n.

2, 5, 17, 59, 223, 757, 2633, 8969, 30431, 102191, 341357, 1134043, 3749633, 12351797, 40558519, 132820211, 433927019, 1414734187, 4604123551, 14959716349, 48537631577, 157280263711, 509055969293, 1645881130301, 5316347779363, 17157165731437, 55325548493311, 178271206357499

Offset

0,1

Comments

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

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

Links

Daniel Suteu, Table of n, a(n) for n = 0..36

Formula

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

Example

a(0) = 2 since 2*1 > 1 = 10^0;
a(1) = 5 since 5*3 = 15 > 10^1;
a(2) = 17 since 17*6 = 102 > 10^2;
a(3) = 59 since 59*17 = 1003; etc.

Mathematica

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

Prog

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

Crossrefs

Cf. A000040, A090977.

Sequence in context: A149998 A149999 A148414 * A232217 A150000 A150001

Adjacent sequences: A306583 A306584 A306585 * A306587 A306588 A306589

Keyword

nonn

Author

Robert G. Wilson v, Feb 25 2019

Status

approved