A187719 Smallest number that when squared is congruent to 41 mod 10^n.

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

Offset

1,2

Comments

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

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