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

Author

Henry Bottomley, Feb 20 2001

Keywords

• base
• easy
• nonn
• look

Examples

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

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

Crossrefs

Cf. A004520, A059692, A169889, A169963.

See A087019 (lunar squares) for another version.

Programs

PARI

a(n) = fromdigits(Vec(Pol(digits(n))^2)%10) \\ Ruud H.G. van Tol, Dec 07 2022

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