A232113 a(n) is the Manhattan distance between n and 2*n in a square spiral of positive integers with 1 at the center.

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

Offset: 1

Author

Alex Ratushnyak, Nov 19 2013

Keywords

• nonn

Comments

Spiral begins:

.

49 26--27--28--29--30--31

| | |

48 25 10--11--12--13 32

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47 24 9 2---3 14 33

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46 23 8 1 4 15 34

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45 22 7---6---5 16 35

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44 21--20--19--18--17 36

| |

43--42--41--40--39--38--37

.

Numbers n such that a(n)^2=n: 1, 4, 16, 625, 20736, 707281, 24010000, 815730721, ...; that is, 1, 4, 2^4, 5^4, 12^4, 29^4, 70^4, 169^4, ... (cf. Pell numbers: A000129).

Crossrefs

Cf. A000129, A214526, A232114, A232115.