A047893 - OEIS (original) (raw)

1, 1, 2, 4, 5, 7, 9, 11, 13, 15, 17, 20, 22, 25, 27, 30, 32, 35, 38, 41, 44, 46, 49, 52, 55, 58, 61, 64, 68, 71, 74, 77, 80, 84, 87, 90, 94, 97, 100, 104, 107, 111, 114, 118, 121, 125, 128, 132, 135, 139, 143, 146, 150, 154, 157, 161, 165, 168, 172, 176, 180, 183

REFERENCES

J. Peters and J. Stein, Mathematische Tafeln, Revised Russian Edition, Moscow, 1968.

FORMULA

a(n) = A055642([A000364](/A000364 "Euler (or secant or "Zig") numbers: e.g.f. (even powers only) sec(x) = 1/cos(x).")(n)) = floor(log_10(|E(2n)|)) + 1 for n >=2, where E is Euler's E function.

EXAMPLE

a(4) = floor(log_10(1385)) + 1 = 4, E(4) = 1385, the 4th Euler number.

MATHEMATICA

a[n_] := IntegerLength[EulerE[2*n]]; Array[a, 100] (* Amiram Eldar, Mar 20 2025 *)

PROG

(PARI) a(n) = #Str(subst(bernpol(2*n+1), 'x, 1/4)*4^(2*n+1)*(-1)^(n+1)/(2*n+1));