A135319 - OEIS

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A135319

a(n) is the first digit after the decimal point in the decimal expansion of log_10(n), i.e., of the Briggsian logarithm of n.

0, 3, 4, 6, 6, 7, 8, 9, 9, 0, 0, 0, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9

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OFFSET

1,2

REFERENCES

Erwin Voellmy, Fünfstellige Logarithmen und Zahlentafeln, 15th edition, Orell Foessli Verlag, Zurich (1962).

LINKS

Table of n, a(n) for n=1..99.

Wikipedia, Common logarithm

FORMULA

a(n) = floor(10*(log_10(n) - floor(log_10(n)))).

EXAMPLE

a(6) = 7, because log_10(6) = 0.77815...