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

Author

Federico Ramondino, Dec 29 2005

Keywords

• nonn

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

Examples

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

Crossrefs

Cf. A000217, A000290.

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

Programs

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

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