A241217 Largest number that when multiplied by 7 produces an n-digit number.

1, 14, 142, 1428, 14285, 142857, 1428571, 14285714, 142857142, 1428571428, 14285714285, 142857142857, 1428571428571, 14285714285714, 142857142857142, 1428571428571428, 14285714285714285, 142857142857142857, 1428571428571428571, 14285714285714285714

Offset

1,2

Comments

The definition "largest number that when multiplied by 3 produces an n-digit number" gives A002277.

References

Albert H. Beiler, Recreations in the theory of numbers, New York, Dover, (2nd ed.) 1966. See Table 34 at p. 62.

Links

Table of n, a(n) for n=1..20.

Index entries for linear recurrences with constant coefficients, signature (11,-10,-1,11,-10).

Formula

a(n) = floor(10^n/7). - Michel Marcus, Apr 21 2014

G.f.: x*(1+3*x-2*x^2+7*x^3)/((x-1)*(10*x-1)*(x+1)*(x^2-x+1)). - Alois P. Heinz, Apr 30 2014

E.g.f.: (3*cosh(10*x) - 7*cosh(x) + 2*exp(x/2)*(2*cos(sqrt(3)*x/2) + sqrt(3)*sin(sqrt(3)*x/2)) - 14*sinh(x) + 3*sinh(10*x))/21. - Stefano Spezia, Jul 31 2024

Example

14*7 = 98 but 15*7 = 105 (too large) so a(2) = 14.

Mathematica

LinearRecurrence[{11, -10, -1, 11, -10}, {1, 14, 142, 1428, 14285}, 30] (* Harvey P. Dale, Mar 03 2024 *)

Prog

(PARI) a(n) = floor(10^n/7); \\ Michel Marcus, Apr 21 2014

Crossrefs

Cf. A020806, A002277.

Sequence in context: A011548 A039916 A378625 * A159500 A167834 A238473

Adjacent sequences: A241214 A241215 A241216 * A241218 A241219 A241220

Keyword

nonn,base,easy

Author

J. Lowell, Apr 17 2014

Extensions

More terms from Michel Marcus, Apr 21 2014

Status

approved