A059729 Carryless squares n X n base 10.

0, 1, 4, 9, 6, 5, 6, 9, 4, 1, 100, 121, 144, 169, 186, 105, 126, 149, 164, 181, 400, 441, 484, 429, 466, 405, 446, 489, 424, 461, 900, 961, 924, 989, 946, 905, 966, 929, 984, 941, 600, 681, 664, 649, 626, 605, 686, 669, 644, 621, 500, 501, 504, 509, 506, 505

Offset

0,3

Links

Seiichi Manyama, Table of n, a(n) for n = 0..9999

David Applegate, Marc LeBrun and N. J. A. Sloane, Carryless Arithmetic (I): The Mod 10 Version.

Index entries for sequences related to carryless arithmetic

Example

a(87) is carryless sum of (6)400, (5)60, (5)60 and (4)9, i.e., 400+20+9 = 429.

Prog

(Python)
def A059729(n):
    s = [int(d) for d in str(n)]
    l = len(s)
    t = [0]*(2*l-1)
    for i in range(l):
        for j in range(l):
            t[i+j] = (t[i+j] + s[i]*s[j]) % 10
    return int("".join(str(d) for d in t)) # Chai Wah Wu, Jun 29 2020
(PARI) a(n) = fromdigits(Vec(Pol(digits(n))^2)%10) \\ Ruud H.G. van Tol, Dec 07 2022

Crossrefs

Cf. A004520, A059692, A169889, A169963.

See A087019 (lunar squares) for another version.

Sequence in context: A008959 A316347 A169917 * A184988 A108533 A200414

Adjacent sequences: A059726 A059727 A059728 * A059730 A059731 A059732

Keyword

base,easy,nonn,look

Author

Henry Bottomley, Feb 20 2001

Status

approved