A053014 a(n) is the smallest number which has n consecutive divisors k, k+1, ..., k+n-1 such that the quotients all begin with the same digit.

1, 30, 60, 840, 10080, 110880, 1441440, 15135120, 21162960, 21162960, 232792560, 26771144400, 26771144400, 2730656728800, 30278164316400, 33977306563200, 38000934972000, 3610088822340000, 37400520199442400, 390033996365613600, 438120379479182400, 4505020423775071200

Offset

1,2

Comments

The smallest values of k corresponding to the first 22 terms are 1, 2, 4, 5, 6, 6, 8, 8, 12, 12, 12, 14, 14, 14, 16, 18, 20, 19, 19, 20, 22, 24. Since m > 0 and 2*m never share the first digit, k is always greater than or equal to n. - Giovanni Resta, May 14 2020

Links

Table of n, a(n) for n=1..22.

Denis Borris, Close Divisors, Ken Duisenberg's Puzzle of the Week, Feb 20 2000.

Example

a(4)=840 since 840/5=168, 840/6=140, 840/7=120 and 840/8=105 all start with 1.

Crossrefs

Cf. A000142.

Sequence in context: A064783 A228877 A258879 * A042784 A042786 A042782

Adjacent sequences: A053011 A053012 A053013 * A053015 A053016 A053017

Keyword

nonn,base

Author

Henry Bottomley, Feb 22 2000

Extensions

a(1) prepended and a(11)-a(22) added by Giovanni Resta, May 14 2020

Status

approved