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A273230 Squares that remain squares if you decrease them by 3 times a repunit with the same number of digits. 3
4, 49, 529, 4489, 38809, 344569, 363609, 375769, 444889, 558009, 597529, 700569, 7198489, 35366809, 44448889, 65983129, 4444488889, 5587114009, 83574762649, 335330171929, 359763638809, 390241344249, 403831017529, 407200963129, 435775577689, 444444888889, 453557800089 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Apart from the initial term, any number ends in 9.

LINKS

Giovanni Resta, Table of n, a(n) for n = 1..10000

EXAMPLE

4 - 3*1 = 1 = 1^2;

49 - 3*11 = 16 = 4^2;

529 - 3*111 = 196 = 14^2.

MAPLE

P:=proc(q, h) local n; for n from 1 to q do

if type(sqrt(n^2-h*(10^(ilog10(n^2)+1)-1)/9), integer) then print(n^2);

fi; od; end: P(10^9, 3);

MATHEMATICA

sol[k_] := Block[{x, e = IntegerLength@k, d = Divisors@ k}, Union[ #+k/# & /@ Select[ Take[d, Ceiling[ Length@d/2]], EvenQ[x = #+k/#] && IntegerLength[ x^2/4] == e &]]^2/4]; r[n_] := 3 (10^n-1)/9; Flatten[sol /@ r /@ Range[12]] (* Giovanni Resta, May 18 2016 *)

CROSSREFS

Cf. A002275, A061844, A273229, A273231-A273234.

Sequence in context: A053769 A173038 A198971 * A199028 A189146 A086094

Adjacent sequences:  A273227 A273228 A273229 * A273231 A273232 A273233

KEYWORD

nonn,easy,base

AUTHOR

Paolo P. Lava, May 18 2016

STATUS

approved

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Last modified May 22 15:37 EDT 2017. Contains 286877 sequences.