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A288854 The unique longest sequence of squares where each number (after the first) is obtained by prefixing a single digit to its predecessor. 0
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

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

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Last modified July 2 03:47 EDT 2022. Contains 354985 sequences. (Running on oeis4.)