A236347 Manhattan distances between n and 2*n in a left-aligned triangle with next M natural numbers in row M: 1, 2 3, 4 5 6, 7 8 9 10, etc.

1, 1, 2, 2, 3, 3, 4, 3, 2, 3, 2, 3, 4, 5, 6, 5, 6, 7, 5, 4, 3, 9, 4, 3, 4, 5, 6, 10, 5, 6, 7, 8, 9, 8, 7, 6, 10, 11, 12, 6, 5, 4, 5, 6, 7, 4, 5, 6, 7, 8, 9, 10, 12, 11, 10, 10, 11, 12, 13, 14, 9, 8, 7, 6, 5, 6, 17, 18, 6, 5, 6, 7, 8, 9, 10, 11, 16, 15, 9, 10, 11, 12

Offset

1,3

Links

Table of n, a(n) for n=1..82.

Example

Triangle in which we find distances begins:
_1
_2  3
_4  5  6
_7  8  9 10
11 12 13 14 15
16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44 45

Prog

(Python)
import math
def getXY(n):
  y = int(math.sqrt(n*2))
  if n<=y*(y+1)/2: y-=1
  x = n - y*(y+1)/2
  return x, y
for n in range(1, 88):
  ox, oy = getXY(n)
  nx, ny = getXY(2*n)
  print str(abs(nx-ox)+abs(ny-oy))+', ',

Crossrefs

Cf. A232113, A236345, A236346.

Sequence in context: A237817 A306949 A189025 * A045430 A067693 A322006

Adjacent sequences: A236344 A236345 A236346 * A236348 A236349 A236350

Keyword

nonn

Author

Alex Ratushnyak, Jan 23 2014

Status

approved