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
KEYWORD
nonn,base
AUTHOR
EXTENSIONS
More terms from Patrick De Geest, March 1999
STATUS
approved