

A236346


Manhattan distances between n^2 and (n+1)^2 in a leftaligned 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(m1) 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

Table of n, a(n) for n=1..68.


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(nxox)+abs(nyoy))+', ',


CROSSREFS

Cf. A236345, A005843, A000027.
Sequence in context: A080820 A274687 A234604 * A306890 A116549 A268382
Adjacent sequences: A236343 A236344 A236345 * A236347 A236348 A236349


KEYWORD

nonn,easy


AUTHOR

Alex Ratushnyak, Jan 23 2014


STATUS

approved



