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A236346 Manhattan distances between n^2 and (n+1)^2 in a left-aligned triangle with next M natural numbers in row M: 1, 2 3, 4 5 6, 7 8 9 10, etc. 2
2, 3, 4, 4, 5, 6, 6, 8, 7, 10, 8, 9, 12, 10, 14, 11, 12, 16, 13, 18, 14, 20, 15, 16, 22, 17, 24, 18, 19, 26, 20, 28, 21, 22, 30, 23, 32, 24, 34, 25, 26, 36, 27, 38, 28, 29, 40, 30, 42, 31, 44, 32, 33, 46, 34, 48, 35, 36, 50, 37, 52, 38, 54, 39, 40, 56, 41, 58 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
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
Subsequence of terms such that a(m)>=a(m-1) and a(m)>=a(m+1) seems to be A005843 (even numbers) except first two terms, and if such a(m) are removed, the remainder seems to be A000027 (natural numbers) except 1:
2, 3, *4*, 4, 5, *6*, 6, *8*, 7, *10*, 8, 9, *12*, 10, *14*, 11, 12, *16*, 13, *18*, 14, *20*, 15, ...
LINKS
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, 77):
ox, oy = getXY(n*n)
nx, ny = getXY((n+1)**2)
print str(abs(nx-ox)+abs(ny-oy))+', ',
CROSSREFS
Sequence in context: A356994 A274687 A234604 * A306890 A116549 A268382
KEYWORD
nonn,easy
AUTHOR
Alex Ratushnyak, Jan 23 2014
STATUS
approved

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Last modified April 22 18:29 EDT 2024. Contains 371906 sequences. (Running on oeis4.)