

A187719


Smallest number that when squared is congruent to 41 mod 10^n.


2



1, 21, 71, 1179, 2429, 47571, 1296179, 8703821, 26452429, 526452429, 13241296179, 19473547571, 2263241296179, 2480526452429, 67263241296179, 932736758703821, 4067263241296179, 38602480526452429, 461397519473547571
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OFFSET

1,2


COMMENTS

41 is the smallest number that is not a perfect square for which a sequence like this is welldefined. 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


LINKS

Charles R Greathouse IV, Table of n, a(n) for n = 1..1000


EXAMPLE

71 qualifies because 71^2 is 5041 which ends in 041.


MATHEMATICA

Table[Solve[x^2 == 41 && Modulus == 10^n, x, Mode > Modular][[1, 2, 2]], {n, 21}] (* T. D. Noe, Mar 22 2011 *)


PROG

(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


CROSSREFS

Cf. A188173.
Sequence in context: A296035 A102233 A309903 * A156285 A160435 A240824
Adjacent sequences: A187716 A187717 A187718 * A187720 A187721 A187722


KEYWORD

nonn,easy


AUTHOR

J. Lowell, Mar 18 2011


STATUS

approved



