A169920 a(n) = n*n in the arithmetic where digits are multiplied in base 10 (as usual) but when digits are to be added they are also multiplied in base 10.

0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 111, 144, 199, 306, 455, 646, 179, 424, 731, 400, 441, 564, 769, 1126, 505, 606, 829, 1124, 1481, 900, 991, 12640, 17190, 1066, 1355, 1086, 1259, 1304, 1651, 1000, 3440, 6120, 1749, 2126, 2605, 2886, 3569, 3864, 4841

Offset

0,3

Comments

How should the carry digits be handled? In this version they have been handled by simply adding them in the old way, which is a bit worrisome. For example, in the calculation below, when the column containing 5 and 4 is "added", i.e. multiplied, there is a carry of 2, which here has been added to the 1 to get 3.

Links

David Consiglio, Jr., Table of n, a(n) for n = 0..10000

Example

a(14) = 14*14 = 306:
....14
....14
------
....56
...14.
------
...306
------

Prog

(Python)
from math import prod
def A169920(m):
    n = len(str(m*m))+1
    hold = list(zip(*[list(str(int(b)*m).ljust(n-1-a, "X").rjust(n-1, "X")) for a, b in enumerate(str(m))]))#List of products of long multiplication
    store = []
    for a, c in enumerate(hold):
        if c.count('X') == len(c):
            store.append(0)
        else:
            store.append(prod([int(b) for b in c if b.isdigit()])*10**(len(hold)-a-1))
    return(sum(store))
# David Consiglio, Jr., Oct 21 2022

Crossrefs

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

Sequence in context: A292679 A357632 A106545 * A093837 A194148 A162497

Adjacent sequences: A169917 A169918 A169919 * A169921 A169922 A169923

Keyword

nonn,base

Author

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

Extensions

More terms from David Consiglio, Jr., Oct 21 2022

Status

approved