A288854 The unique longest sequence of squares where each number (after the first) is obtained by prefixing a single digit to its predecessor.

25, 625, 5625, 75625, 275625

Offset: 1

Author

Bernard Schott, Jun 18 2017

Keywords

• nonn
• fini
• full
• base

Comments

This chain with five squares is the longest which exists in this context, there is no such sequence of length >= 6.

There are also only four chains of maximal length 4 with:

-> 25, 225, 1225, 81225. These four squares are the first terms of A061839.

-> 25, 225, 4225, 34225.

-> 25, 225, 7225, 27225. These four squares are the first terms of A191486.

-> 25, 625, 5625, 15625.

There are also only three chains of maximal length 3 with:

-> 3025, 93025, 893025.

-> 30625, 330625, 3330625.

-> 50625, 950625, 4950625.

See Crux Mathematicorum links.

Examples

			25 = 5^2; 625 = 25^2; 5625 = 75^2; 75625 = 275^2; 275625 = 525^2.
		

Links

• L. Csirmaz, Problem 526, solution, Crux Mathematicorum, page 280, Vol.7, Nov. 81.
• Friend H. Kierstead, Jr., Problem 526, partial solution, Crux Mathematicorum, page 87, Vol.7, Mar. 81.

Crossrefs

Cf. A061839, A191486.