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A035126
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Squares when digits rotated right once remain square.
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4
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1, 4, 9, 256, 441, 961, 16641, 48841, 61009, 66564, 1127844, 2537649, 3857296, 4932841, 182682256, 298840369, 342842256, 392872041, 493772841, 787588096, 877996161, 10766967696, 33255899044, 49382172841, 74825772849
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,2
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COMMENTS
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Those resulting in leading zeros excluded.
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LINKS
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Chai Wah Wu, Table of n, a(n) for n = 1..1838
Eric Weisstein's World of Mathematics, Square Number
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FORMULA
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a(n) = A045877(n)^2. - R. J. Mathar, Jan 25 2017
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EXAMPLE
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2221^2 = 4932841 -> 1493284 = 1222^2. Note that the root behaves accordingly!
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MATHEMATICA
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Select[Range[300000]^2, IntegerQ[Sqrt[FromDigits[RotateRight[ IntegerDigits[ #]]]]]&] (* Harvey P. Dale, Mar 22 2015 *)
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PROG
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(MAGMA) [k:k in [m^2:m in [1..10^6]]| IsSquare(Seqint( (Intseq(Floor(k/10)) cat [ Intseq(k)[1]])))]; // Marius A. Burtea, Oct 08 2019
(Python)
from itertools import count, islice
from sympy.solvers.diophantine.diophantine import diop_DN
def A035126_gen(): # generator of terms
for l in count(0):
l1, l2 = 10**(l+1), 10**l
yield from sorted(set(x**2 for z in (diop_DN(10, m*(1-l1)) for m in range(10)) for x, y in z if l1 >= x**2 >= l2))
A035126_list = list(islice(A035126_gen(), 30)) # Chai Wah Wu, Apr 23 2022
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CROSSREFS
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Cf. A045877, A035130.
Sequence in context: A299122 A167657 A175700 * A178454 A051671 A109103
Adjacent sequences: A035123 A035124 A035125 * A035127 A035128 A035129
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KEYWORD
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nonn,base
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AUTHOR
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Patrick De Geest, Nov 15 1998
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STATUS
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approved
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