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A187719
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Smallest number that when squared is congruent to 41 mod 10^n.
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2
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1, 21, 71, 1179, 2429, 47571, 1296179, 8703821, 26452429, 526452429, 13241296179, 19473547571, 2263241296179, 2480526452429, 67263241296179, 932736758703821, 4067263241296179, 38602480526452429, 461397519473547571
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OFFSET
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1,2
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COMMENTS
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41 is the smallest number that is not a perfect square for which a sequence like this is well-defined. For 24, the sequence is 2,18,32 and then terminates because no square ends in 0024.
41 is the first term of A188173, which lists other numbers with this property. - T. D. Noe, Mar 23 2011
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LINKS
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Charles R Greathouse IV, Table of n, a(n) for n = 1..1000
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EXAMPLE
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71 qualifies because 71^2 is 5041 which ends in 041.
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MATHEMATICA
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Table[Solve[x^2 == 41 && Modulus == 10^n, x, Mode -> Modular][[1, 2, 2]], {n, 21}] (* T. D. Noe, Mar 22 2011 *)
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PROG
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(Sage)
def A187719(n):
bposs = [0]
works = lambda x, j: (x^2) % (10^j) == 41 % (10^j)
for w in [0..n]:
bposs = list((i*10**w+b) for i, b in cartesian_product([[0..9], bposs]))
bposs = list(b for b in bposs if works(b, w))
final = list(b for b in bposs if works(b, n))
if final: return min(final) # D. S. McNeil, Mar 22 2011
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CROSSREFS
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Cf. A188173.
Sequence in context: A296035 A102233 A309903 * A156285 A160435 A240824
Adjacent sequences: A187716 A187717 A187718 * A187720 A187721 A187722
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KEYWORD
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nonn,easy
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AUTHOR
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J. Lowell, Mar 18 2011
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STATUS
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approved
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