A169921 a(n) = n*n in the arithmetic where when digits are to be added they are multiplied, and when they are to be multiplied they are added.

0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 210, 242, 294, 366, 458, 620, 762, 924, 2906, 3018, 440, 492, 564, 656, 768, 960, 1122, 4904, 5016, 5128, 690, 762, 854, 966, 1098, 1320, 6902, 7014, 7126, 7238, 960, 1052, 1164, 1296, 1448, 8900, 9012, 9124, 9236, 9348

Offset

0,2

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 7 and 6 is "added", i.e. multiplied, there is a carry of 4, which here has been added to the 2 to get 6.

Links

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

Example

a(15) = 15*15 = 620:
....15
....15
------
....70
...26.
------
...620
------

Prog

(Python)
from math import prod
def A169921(m):
    n = len(str(m))+1
    hold = [x for x in list(zip(*[list(str(sum((int(b)+int(d))*10**a for a, b in enumerate(reversed(str(m))))).ljust(c+n, "X").rjust(8, "X")) for c, d in enumerate(reversed(str(m)))])) if x != ('X', )*(n-1)]
    store = [prod([int(b) for b in c if b.isdigit()])*10**a for a, c in enumerate(reversed(hold))]
    return sum(store)
# David Consiglio, Oct 24 2022

Crossrefs

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

Sequence in context: A343335 A110725 A100800 * A169919 A292512 A248195

Adjacent sequences: A169918 A169919 A169920 * A169922 A169923 A169924

Keyword

nonn,base

Author

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

Extensions

More terms from David Consiglio, Jr., Oct 24 2022

Status

approved