

A249587


Numbers whose square remains square when the initial digit is removed.


4



1, 2, 3, 7, 8, 9, 10, 15, 20, 25, 30, 35, 45, 55, 65, 70, 75, 80, 85, 90, 95, 100, 125, 150, 165, 175, 185, 200, 205, 225, 245, 250, 265, 275, 285, 300, 305, 325, 350, 450, 525, 550, 575, 650, 700, 750, 775, 800, 850, 900, 945, 950, 975, 985, 1000, 1025, 1250, 1425, 1500, 1650, 1750, 1825, 1850, 2000, 2050, 2225, 2250, 2450, 2500
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OFFSET

1,2


COMMENTS

The squares are in A225885.
The first three terms have a singledigit square which by convention yields 0 if the first digit is removed. The first 6 terms are the only terms of the sequence not divisible by 5.


LINKS

Chai Wah Wu, Table of n, a(n) for n = 1..5000


MATHEMATICA

b /. Flatten[Outer[Solve[a^2 + #2*10^#1 == b^2 && 0 <= a < Sqrt[10^#1] && Sqrt[#2*10^#1] <= b < Sqrt[10^(#1 + 1)], {a, b}, Integers] &, Range[0, 5], Range[9]], 2] (* Davin Park, Dec 30 2016 *)
Sqrt[#]&/@Select[Range[2500]^2, IntegerQ[Sqrt[FromDigits[ Rest[ IntegerDigits[ #]]]]]&] (* Harvey P. Dale, May 01 2017 *)


PROG

(PARI) is(n)=issquare(n^2%10^(#Str(n^2)1))


CROSSREFS

Cf. A225873. See also A227916.
Sequence in context: A037461 A284514 A268398 * A007607 A076682 A327224
Adjacent sequences: A249584 A249585 A249586 * A249588 A249589 A249590


KEYWORD

nonn,base


AUTHOR

M. F. Hasler, Nov 01 2014


STATUS

approved



