A345328 a(n) is the smallest integer k>1 such that |log(k)-round(log(k))| is smaller than 10^(-n).

3, 20, 1096, 2981, 59874, 442413, 8886110, 65659969, 178482301, 3584912846, 26489122130, 195729609429, 3931334297144, 78962960182680, 214643579785916, 4311231547115195, 31855931757113756, 86593400423993747, 12851600114359308275, 34934271057485095348

Offset: 1

Author

Andrzej Kukla, Jun 14 2021

Keywords

• nonn

Comments

In other words, a(n) is the smallest integer k>1 such that the distance between log(k) and nearest integer to log(k) is smaller than 10^(-n).

Examples

			For n=4 a(n)=2981, because 2981 is the smallest integer greater than 1 such that |log(2981)-round(2981)| = 0.00001409... < 10^(-4).
		

Crossrefs

Cf. A000193, A000227, A079663, A080021.

Programs

Maple

n := 1: for i from 2 to 10^10 do if abs(evalf(log(i)) - floor(log(i) + 1/2)) < 10^(-n) then print(i); n := n + 1 fi end do;

PARI

\\ suitable precision needed.
a(n)={my(epsilon=1.0/10^n); for(k=1, oo, my(t=floor(exp(k))); if(k-log(t)Andrew Howroyd, Jun 14 2021

Extensions

Terms a(10) and beyond from Andrew Howroyd, Jun 14 2021