A145848 -id:A145848 - cp's OEIS frontend

A146991 a(n)=sqrt(A145848(n)).

7, 41, 380, 475, 506, 570, 759, 4901, 36050, 39845, 48700, 49964, 50281, 54075, 55973, 72100, 74946, 79690, 90125, 99928, 499001, 3200225, 3247660, 3497480, 3747300, 3905413, 3997120, 4246940, 4623250, 4803500, 4999561, 5002724

Offset: 1

Zak Seidov, Nov 04 2008

nonn

A145848 [From Zak Seidov, Nov 05 2008]

A146993 Number of terms in A145848 with exactly 2n decimal digits.

Original entry on oeis.org

1, 1, 5, 1, 12, 1, 24, 2, 47, 2, 53, 1, 70, 1

Offset: 1

Zak Seidov, Nov 04 2008

It is shown by I. Bernshtein, see link, that a(2n+1)>=1 and 1<=a(2n)<=2. Thanks to Tanya Khovanova for this link.

I. Bernshtein, Solution of problem M460.

Cf. A145848, A146991.

Definition, comment, and a(11) corrected, and a(12)-a(14) added, by Jon E. Schoenfield, Nov 19 2008

A147608 Squares which are concatenation of two positive squares with possible intervening zeros.

Original entry on oeis.org

49, 169, 361, 1225, 1444, 1681, 3249, 4225, 4900, 9025, 15625, 16900, 36100, 42025, 49729, 64009, 81225, 93025, 105625, 122500, 144400, 168100, 225625, 237169, 256036, 324900, 422500, 490000, 519841, 576081, 819025, 902500, 950625, 970225

Offset: 1

Zak Seidov, Nov 08 2008

A145848 is a subsequence.

			324 = 18^2, 9 = 3^2, 3249 = 324:9 = 57^2.
9 = 3^2, 25 = 5^2, 9025 = 9:0:25 = 95^2 (intervening zero).

David W. Wilson, Table of n, a(n) for n = 1..1000

Cf. A039686 (variant with no intervening zeros).

Cf. A145848 (squares with an even number of digits, where the first half is a square and the second half is a nonzero square).

s={}; Do[n2=n*n; id=IntegerDigits[n2]; Le=Length[id]; Do[If[IntegerQ/@Sqrt[FromDigits/@{Take[id,k], Drop[id,k]}] == {True,True}, If[FromDigits@Drop[id,k]>0, Print[n2]; AppendTo[s,n2]; Break[]]], {k,1,Le-1}], {n,4,10^4}]

Edited by Charles R Greathouse IV, Apr 24 2010

Definition corrected by David W. Wilson, Nov 22 2012

A216233 Numbers whose squares have 2R-1 digits, such that the number represented by leftmost R digits and number represented by rightmost R digits divide each other evenly.

Original entry on oeis.org

245, 249, 251, 255, 264, 1245, 1249, 2490, 2498, 2502, 2510, 10984, 12490, 12498, 15449, 18735, 18751, 18868, 22714, 24980, 24996, 27907, 28302, 31225, 31249, 31579, 101852, 124996, 139535, 152174, 187494, 187510, 218751, 238165, 249992, 279070, 281249

Offset: 1

Thomas S. Pedigo, Mar 14 2013

Trivial solutions where the rightmost R digits are all zeros have been omitted. The first indices k for which the rightmost R digits of a(k)^2 do not contain leading zeros are 5, 12, 15, 19, 26, 27, 30, 34, 39, 52, 53, 62, 67, 80.

			The square of 22714 is 515925796, and 51592 = 2*25796.

Giovanni Resta, Table of n, a(n) for n = 1..165

Cf. A115528, A116501, A145848.

cnt = 0; Do[p = 10^Floor[nd/2]; Do[x = Floor[n*n/p]; y = Mod[n*n, 10*p]; If[y>0 && Mod[x,y]*Mod[y,x] == 0, Print[++cnt, " ", n, " ", n*n]], {n, p, Floor[10^(nd/2)]}], {nd,3,11,2}] (* Giovanni Resta, Mar 15 2013 *)

Missing a(25) and a(27)-a(37) from Giovanni Resta, Mar 15 2013

Comment corrected by Giovanni Resta, Mar 15 2013

A219542 Numbers n such that n^2 is a concatenation of 3 nonzero squares, leading zeros not allowed.

Original entry on oeis.org

12, 21, 37, 44, 107, 108, 120, 129, 191, 204, 209, 210, 223, 306, 315, 342, 343, 345, 370, 408, 413, 440, 501, 642, 696, 804, 955, 959, 982, 995, 1002, 1044, 1063, 1065, 1070, 1080, 1107, 1169, 1200, 1275, 1281, 1290, 1301, 1306, 1315, 1349, 1385, 1503, 1910

Offset: 1

Zak Seidov, Nov 22 2012

			a(1) = 12: 12^2 = 144, 1 = 1^2, 4 = 2^2, 4 = 2^2;
a(1500) = 3176900^2 = 100, 9, 2693610000, 100 = 10^2, 9 = 3^2, 2693610000 = 51900^2.

Zak Seidov, Table of n, a(n) for n = 1..1500

Cf. A039686, A048375, A048646, A145848, A147608.

cp's OEIS Frontend

A146991 a(n)=sqrt(A145848(n)).

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A146993 Number of terms in A145848 with exactly 2n decimal digits.

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A147608 Squares which are concatenation of two positive squares with possible intervening zeros.

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A216233 Numbers whose squares have 2R-1 digits, such that the number represented by leftmost R digits and number represented by rightmost R digits divide each other evenly.

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Programs

Mathematica

Extensions

A219542 Numbers n such that n^2 is a concatenation of 3 nonzero squares, leading zeros not allowed.

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