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A039686 Squares which are the concatenation of two nonzero squares. 8
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified December 3 21:17 EST 2021. Contains 349468 sequences. (Running on oeis4.)