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

1,1

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.

Links

Table of n, a(n) for n=1..5.

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.

Example

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

Crossrefs

Cf. A061839, A191486.

Sequence in context: A207856 A207424 A207739 * A208081 A207209 A207203

Adjacent sequences: A288851 A288852 A288853 * A288855 A288856 A288857

Keyword

nonn,fini,full,base

Author

Bernard Schott, Jun 18 2017

Status

approved