A169919 a(n) = n*n in the arithmetic where digits are added in base 10 (as usual) but when digits are to be multiplied they are also added in base 10.

0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 220, 242, 264, 286, 308, 330, 352, 374, 396, 418, 440, 462, 484, 506, 528, 550, 572, 594, 616, 638, 660, 682, 704, 726, 748, 770, 792, 814, 836, 858, 880, 902, 924, 946, 968, 990, 1012, 1034, 1056, 1078, 1100, 1122, 1144

Offset

0,2

Links

Michael S. Branicky, Table of n, a(n) for n = 0..9999

Example

a(16) = 16*16 = 352:
....16
....16
------
....82
...27.
------
...352
------

Prog

(Python)
def digits(n): return list(map(int, str(n)))
def arith2(m, n):
    s, t, ans = digits(min(m, n))[::-1], digits(max(m, n))[::-1], 0
    for i, si in enumerate(s):
        u, carry = [0 for _ in range(i)], 0
        for ti in t:
            # below, if first + --> *, we obtain regular arithmetic
            carry, ui = divmod(si+ti + carry, 10)
            u.append(ui)
        if carry:
            u.append(carry)
        ans += int("".join(map(str, u))[::-1])
    return ans
def a(n): return arith2(n, n)
print([a(n) for n in range(53)]) # Michael S. Branicky, Jan 03 2022

Crossrefs

The four versions are A000290, A169919, A169920, A169921.

Sequence in context: A110725 A100800 A169921 * A292512 A248195 A094041

Adjacent sequences: A169916 A169917 A169918 * A169920 A169921 A169922

Keyword

nonn,base

Author

David Applegate, Marc LeBrun and N. J. A. Sloane, Jul 20 2010

Extensions

Terms a(17)-a(53) from John W. Layman, Jul 22 2010

Status

approved