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A048375 Numbers n such that n^2 is a concatenation of two nonzero squares. 7
7, 13, 19, 35, 38, 41, 57, 65, 70, 125, 130, 190, 205, 223, 253, 285, 305, 350, 380, 410, 475, 487, 570, 650, 700, 721, 905, 975, 985, 1012, 1201, 1250, 1265, 1300, 1301, 1442, 1518, 1771, 1900, 2024, 2050, 2163, 2225, 2230, 2277, 2402, 2435, 2530, 2850 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Leading zeros not allowed, trailing zeros are.

This means that, e.g., 95 is not in the sequence although 95^2 = 9025 could be seen as concatenation of 9 and 025 = 5^2. - M. F. Hasler, Jan 25 2016

LINKS

Giovanni Resta, Table of n, a(n) for n = 1..3000

FORMULA

a(n) = sqrt(A039686(n)). - M. F. Hasler, Jan 25 2016

EXAMPLE

1771^2 = 3136441 = 3136_441 and 3136 = 56^2, 441 = 21^2.

MATHEMATICA

squareQ[n_] := IntegerQ[Sqrt[n]]; okQ[n_] := MatchQ[IntegerDigits[n^2], {a__ /; squareQ[FromDigits[{a}]], b__ /; First[{b}] > 0 && squareQ[FromDigits[{b}]]}]; Select[Range[3000], okQ] (* Jean-Fran├žois Alcover, Oct 20 2011, updated Dec 13 2016 *)

PROG

(PARI) is_A048375(n)={my(p=100^valuation(n, 10)); n*=n; while(n>p*=10, issquare(n%p)&&issquare(n\p)&&n%p*10>=p&&return(1))} \\ M. F. Hasler, Jan 25 2016

CROSSREFS

Cf. A039686, A048646.

Sequence in context: A122482 A265629 A283191 * A198035 A208720 A208776

Adjacent sequences:  A048372 A048373 A048374 * A048376 A048377 A048378

KEYWORD

nonn,easy,nice,base

AUTHOR

Patrick De Geest, Mar 15 1999

STATUS

approved

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Last modified September 25 01:17 EDT 2018. Contains 315360 sequences. (Running on oeis4.)