A039686 Squares which are the concatenation of two nonzero squares.
49, 169, 361, 1225, 1444, 1681, 3249, 4225, 4900, 15625, 16900, 36100, 42025, 49729, 64009, 81225, 93025, 122500, 144400, 168100, 225625, 237169, 324900, 422500, 490000, 519841, 819025, 950625, 970225, 1024144, 1442401, 1562500
Offset: 1
Examples
1225=35^2, 225=15^2, 1=1^2.
References
- D. Wells, Curious and interesting numbers, Penguin Books, p. 152.
Links
- Giovanni Resta, Table of n, a(n) for n = 1..3000 (first 1000 terms from David W. Wilson)
Crossrefs
Cf. A048375.
Programs
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Haskell
a039686 n = a039686_list !! (n-1) a039686_list = filter ((== 1) . a010052) a191933_list -- Reinhard Zumkeller, Jul 17 2011
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Mathematica
t = Table[n^2, {n, 750}]; f[j_, k_] := Block[{n = j*10^Floor[1 + Log10@ k] + k}, If[IntegerQ@ Sqrt@ n, n, 0]]; Take[ Union@ Flatten@ Table[ f[t[[j]], t[[k]]], {j, 250}, {k, 750}], {2, 33}] (* Robert G. Wilson v, Jul 18 2011 *) squareQ[n_] := IntegerQ[Sqrt[n]]; okQ[n_] := MatchQ[IntegerDigits[n], {a__ /; squareQ[FromDigits[{a}]], b__ /; First[{b}] > 0 && squareQ[FromDigits[ {b}]]}]; Select[Range[2000]^2, okQ] (* Jean-François Alcover, Dec 13 2016 *) -
PARI
is_A039686(n)={my(p=10);until(n<=p*=10,issquare(n%p)&&issquare(n\p)&&n%p*10>=p&&issquare(n)&&return(n>10))} \\ We must check whether n is a square but in practice this will be sure a priori (cf below) so we put this test at the end. The same applies for "n>10". - M. F. Hasler, Jan 25 2016
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PARI
{for(m=4,999, is_A039686(m^2)&&print1(m^2,","))} \\ Here the final checks issquare(n) & n>10 in the above function are superfluous, but they will only be done in the ("few") positive cases. - M. F. Hasler, Jan 25 2016
Formula
a(n) = A048375(n)^2. - M. F. Hasler, Jan 25 2016
Extensions
More terms from Patrick De Geest, March 1999
Comments