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A090925 Permutation of natural numbers arising from a spiral. 6
1, 4, 5, 6, 7, 8, 9, 2, 3, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 10, 11, 12, 13, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 26, 27, 28, 29, 30, 31, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Write out the natural numbers in a square counterclockwise spiral:

17.16.15.14.13

18..5..4..3.12

19..6..1..2.11

20..7..8..9.10

21.22.23.24.25

Now read off the numbers in a counterclockwise spiral: 1 -> 4 -> 5 -> 6 -> 7 -> 8 -> 9 -> 2 -> 3 -> 14 -> etc.

LINKS

Eric M. Schmidt, Table of n, a(n) for n = 1..1000

PROG

(Sage)

def a(n) :

....x = (isqrt(n-1)+1)//2

....return n + 2*x if n + 2*x <= (2*x+1)^2 else n - 6*x

# Eric M. Schmidt, May 18 2016

CROSSREFS

Cf. A020703, A090861, A090915, A090928, A090929, A090930.

Sequence in context: A239440 A248355 A178053 * A143836 A168094 A089166

Adjacent sequences:  A090922 A090923 A090924 * A090926 A090927 A090928

KEYWORD

easy,nonn

AUTHOR

Felix Tubiana (fat2(AT)columbia.edu), Feb 26 2004

EXTENSIONS

Offset corrected by Eric M. Schmidt, May 18 2016

STATUS

approved

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Last modified December 3 21:14 EST 2016. Contains 278745 sequences.