A288854 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

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

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

KEYWORD

nonn,fini,full,base

AUTHOR

STATUS

approved