A112663 Smallest circular sequence of period 32 such that any two adjacent numbers sum to a square number.

1, 8, 28, 21, 4, 32, 17, 19, 30, 6, 3, 13, 12, 24, 25, 11, 5, 31, 18, 7, 29, 20, 16, 9, 27, 22, 14, 2, 23, 26, 10, 15, 1, 8, 28, 21, 4, 32, 17, 19, 30, 6, 3, 13, 12, 24, 25, 11, 5, 31, 18, 7, 29, 20, 16, 9, 27, 22, 14, 2, 23, 26, 10, 15, 1, 8, 28, 21, 4, 32, 17, 19, 30, 6, 3, 13, 12, 24, 25, 11, 5, 31, 18, 7, 29, 20, 16, 9, 27, 22, 14, 2, 23, 26, 10, 15

Offset

0,2

Comments

The terms of this sequence are given in A071984. An algorithm for computing circular chains of squares is given in A090460. - T. D. Noe, Dec 30 2005

Links

Table of n, a(n) for n=0..95.

Formula

a(n) = A272259(32, (n-1) mod 32) for all n, where "mod" is the (nonnegative) remainder operator. - M. F. Hasler, Jun 23 2025

Example

1+8=9
8+28=36
28+21=49
...
26+10=36
10+15=25
15+1=16

Prog

(PARI) apply( {A112663(n)=my(r=1); foreach(digits(403079653644429064719159, 6)[1..n%32], s, r=(s+2)^2-r); r}, [0..77]) \\ M. F. Hasler, Jun 23 2025

Crossrefs

Cf. A000217, A000290.

Cf. A272259 (has terms a(0..31) in row 32).

Sequence in context: A126815 A053619 A272259 * A220288 A201101 A201105

Adjacent sequences: A112660 A112661 A112662 * A112664 A112665 A112666

Keyword

nonn

Author

Federico Ramondino, Dec 29 2005

Status

approved