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 A273229 Squares that remain squares if you decrease them by a repunit with the same number of digits. 3
 1, 36, 400, 3136, 24336, 115600, 118336, 126736, 211600, 309136, 430336, 577600, 5973136, 19713600, 30869136, 53582400, 3086469136, 4310710336, 71526293136, 111155560000, 112104432400, 113531259136, 137756776336, 206170483600, 245996160400, 262303768336, 308642469136 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Apart from the initial term, any number ends in 0 or 6. LINKS Giovanni Resta, Table of n, a(n) for n = 1..10000 EXAMPLE 1 - 1 = 0 = 0^2; 36 - 11 = 25 = 5^2; 400 - 111 = 289 = 17^2; 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, 1); 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_] := (10^n-1)/9; Flatten[sol /@ r /@ Range[12]] (* Giovanni Resta, May 18 2016 *) CROSSREFS Cf. A002275, A061844, A273230-A273234. Sequence in context: A086575 A203027 A164583 * A264361 A055862 A105095 Adjacent sequences: A273226 A273227 A273228 * A273230 A273231 A273232 KEYWORD nonn,easy,base AUTHOR Paolo P. Lava, May 18 2016 STATUS approved

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Last modified December 1 16:30 EST 2023. Contains 367500 sequences. (Running on oeis4.)