A181682 a(n) = smallest number k such that k is divisible by 2^n, k+1 is divisible by 3^n and k+2 is divisible by 5^n.

8, 548, 21248, 561248, 18381248, 212781248, 5315781248, 70925781248, 9912425781248, 364206425781248, 4497636425781248, 465079836425781248, 5779489836425781248, 181155019836425781248, 2572639519836425781248

Offset

1,1

Comments

The sequence a(n) shows an interesting property : a(n) - a(n-1) == 0 mod 10^(n-1), for example a(7) - a(6) = 5103000000 == 0 mod 10^6.

Links

Table of n, a(n) for n=1..15.

Example

a(2) = 548 = 2 ^ 2 * 137 ; 549 = 3 ^ 2 * 61 ; 550 = 2 * 5 ^ 2 * 11.

Maple

with(numtheory): for k from 1 to 4 do: kk:=0:for n from 1 to 600000 do: xx:=2^k:yy:=3^k:
  zz:=5^k:if irem(n, xx) =0 and irem(n+1, yy) =0 and irem(n+2, zz) =0 and kk=0 then
  kk:=1:print(k):print(n):else fi:od:od:

Mathematica

Table[ChineseRemainder[{0, -1, -2}, {2^n, 3^n, 5^n}], {n, 15}]

Crossrefs

Cf. A063528.

Sequence in context: A027536 A334255 A174252 * A248331 A301950 A240300

Adjacent sequences: A181679 A181680 A181681 * A181683 A181684 A181685

Keyword

nonn

Author

Michel Lagneau, Feb 03 2011

Status

approved