A169821 -id:A169821 - cp's OEIS frontend

A170990 Carryless product n X n in base 9.

0, 1, 4, 0, 7, 7, 0, 4, 1, 81, 100, 121, 135, 160, 97, 108, 130, 145, 324, 361, 400, 351, 394, 349, 378, 337, 370, 0, 55, 31, 0, 61, 34, 0, 58, 28, 567, 640, 634, 621, 619, 610, 594, 589, 577, 567, 577, 589, 594, 610, 619, 621, 634, 640, 0, 28, 58, 0, 34, 61, 0, 31, 55, 324, 370

Offset: 0

N. J. A. Sloane, Aug 29 2010

Seiichi Manyama, Table of n, a(n) for n = 0..6560
David Applegate, Marc LeBrun and N. J. A. Sloane, Carryless Arithmetic (I): The Mod 10 Version.
Index entries for sequences related to carryless arithmetic

For bases 2 through 10 see A000695, A169999, A170985-A170990 and A059729. A169821 is a less satisfactory variant.

a(n) = fromdigits(Vec(Pol(digits(n, 9))^2)%9, 9); \\ Seiichi Manyama, Mar 09 2023

A169908 a(n) = n*n in carryless digital root arithmetic in base 10.

Original entry on oeis.org

0, 1, 4, 9, 7, 7, 9, 4, 1, 9, 100, 121, 144, 169, 187, 117, 139, 154, 171, 199, 400, 441, 484, 439, 477, 427, 469, 414, 451, 499, 900, 961, 934, 999, 967, 937, 999, 964, 931, 999, 700, 781, 774, 769, 757, 747, 739, 724, 711, 799, 700, 711, 724, 739, 747, 757

Offset: 0

David Applegate, Marc LeBrun and N. J. A. Sloane, Jul 11 2010

Addition and multiplication are the same as in school, that is, done in base 10, except that there are no carries and when individual digits are added or multiplied the result is replaced by its digital root (A010888).

			14*14 = 187:
..14
..14
----
..47
.14.
----
.187
----

Index entries for sequences related to carryless arithmetic

Cf. A010888, A169821.

A010888 := proc(n)
    if n = 0 then
        0;
    else
        1+modp(n-1,9) ;
    end if;
end proc:
carryLmult1dig := proc(a,b)
    local adigs,cdigs,d,len ;
    if b <= 9 then
        adigs := convert(a,base,10) ;
        len := nops(adigs) ;
        cdigs := [seq( A010888(b*op(d,adigs)) ,d=1..len)] ;
        add(op(d,cdigs)*10^(d-1),d=1..len) ;
    else
        error b,"not smaller than 10" ;
    end if;
end proc:
carryLmult := proc(a,b)
    local adigs,bdigs,c,len ;
    adigs := convert(a,base,10) ;
    bdigs := convert(b,base,10) ;
    len := max(nops(adigs),nops(bdigs)) ;
    c := 0 ;
    for i from 1 to nops(bdigs) do
        carryLmult1dig(a,op(i,bdigs)) ;
        c := carryLadd(c,%*10^(i-1)) ;
    end do:
    c ;
end proc:
A169908 := proc(n)
    carryLmult(n,n) ;
end proc: # R. J. Mathar, Jul 12 2013

cp's OEIS Frontend

A170990 Carryless product n X n in base 9.

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