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

1,1

Comments

Intersection of A191933 and A000290; A193095(a(n))>0 and A010052(a(n))=1. - Reinhard Zumkeller, Jul 17 2011

Note that "leading zeros" are not allowed, e.g., 9025 = 95^2 is not in the sequence although it is the concatenation of 9 = 3^2 and 025 = 5^2. - M. F. Hasler, Jan 25 2016

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)

Formula

a(n) = A048375(n)^2. - M. F. Hasler, Jan 25 2016

Example

1225=35^2, 225=15^2, 1=1^2.

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 *)

Prog

(Haskell)
a039686 n = a039686_list !! (n-1)
a039686_list = filter ((== 1) . a010052) a191933_list
-- Reinhard Zumkeller, Jul 17 2011
(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
(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

Crossrefs

Cf. A048375.

Sequence in context: A277793 A147608 A258060 * A038628 A244695 A244179

Adjacent sequences: A039683 A039684 A039685 * A039687 A039688 A039689

Keyword

nonn,base

Author

Felice Russo

Extensions

More terms from Patrick De Geest, March 1999

Status

approved