A063528 -id:A063528 - cp's OEIS frontend

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

Michel Lagneau, Feb 03 2011

nonn

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.

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

Cf. A063528.

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:

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

A069022 Start of the first occurrence of two consecutive numbers divisible by an n-th power.

Original entry on oeis.org

1, 8, 80, 80, 1215, 16767, 76544, 636416, 3995648, 24151040, 36315135, 689278976, 1487503359, 1487503359, 155240824832, 785129144319, 4857090670592, 45922887663615, 157197025673216, 1375916505694208, 2280241934368767

Offset: 1

Amarnath Murthy, Apr 02 2002

nonn

Essentially the same as A063528. [R. J. Mathar, Sep 29 2008]

			(8, 9) is the first occurrence of two consecutive numbers divisible by a square, so a(2) = 8.

Cf. A069021.

a = {1, 1}; k = 4; Do[ While[Min[a] < n, k++; a = Drop[a, 1]; a = Append[ a, Max[ Transpose[ FactorInteger[k]] [[2]] ]]]; Print[k - 1], {n, 2, 9}] (* Robert G. Wilson v *)

More terms from Larry Reeves (larryr(AT)acm.org), Oct 12 2003

cp's OEIS Frontend

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.

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