A107929 Smallest list of integers from 1 to n such that sum of any two adjacent terms is a square.

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

Offset: 1

Author

Zak Seidov, Jun 11 2005

Keywords

• fini
• full
• nonn

Comments

This "solution" holds also for numbers 0 to n=15: it is sufficient to put zero at the end of the sequence. The same is true for cases n=16 and 17: {8,1,15,10,6,3,13,12,4,5,11,14,2,7,9,16} (add zero at the end or between 9 and 16 which gives two solutions), {16,9,7,2,14,11,5,4,12,13,3,6,10,15,1,8,17} (add zero at the beginning or between 16 and 9 which gives two solutions). Also, for n=23 (next case with 1-to-n solution), we have 4 0-to-n solutions, etc. Cf. A090461 = numbers n such that there is a permutation of the numbers 1 to n such that the sum of adjacent numbers is a square; A090461 = numbers n such that there is a permutation of the numbers 1 to n such that the sum of adjacent numbers is a square.

Examples

			8+1=9, 1+15=16, 15+10=25, 10+6=16, 6+3=9, 3+13=16, 13+12=25, 12+4=16, 4+5=9, 5+11=16, 11+14=25, 14+2=16, 2+7=9, 7+9=16 all 14 sums are squares.
		

Crossrefs

Cf. A090460, A090461, A071983.