A232114 a(n) is the Manhattan distance between n and n^2 in a square spiral of positive integers with 1 at the center.

0, 2, 2, 2, 6, 4, 6, 8, 6, 12, 8, 12, 12, 12, 16, 12, 20, 14, 20, 18, 20, 22, 20, 26, 20, 30, 22, 30, 26, 30, 30, 30, 34, 30, 38, 30, 42, 32, 42, 36, 42, 40, 42, 44, 42, 48, 42, 52, 42, 56, 44, 56, 48, 56, 52, 56, 56, 56, 60, 56, 64, 56, 68, 56, 72, 58, 72, 62, 72, 66

Offset

1,2

Comments

Spiral begins:

.

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

| | |

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

| | | | |

47 24 9 2---3 14 33

| | | | | | |

46 23 8 1 4 15 34

| | | | | |

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

| | | |

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

| |

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

.

Numbers n such that a(n)=n: 2, 8, 12, 22, 30, 44, 56, 74, 90, 112, 132, 158, 182, 212, 240, 274, 306, 344, 380, 422, ... That is, 2 * A084263.

Links

Table of n, a(n) for n=1..70.

Crossrefs

Cf. A000290, A084263, A214526, A232113, A232115.

Sequence in context: A099259 A131904 A278264 * A038074 A059885 A259689

Adjacent sequences: A232111 A232112 A232113 * A232115 A232116 A232117

Keyword

nonn

Author

Alex Ratushnyak, Nov 19 2013

Status

approved