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

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

0,3

Comments

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).

Links

Table of n, a(n) for n=0..55.

Index entries for sequences related to carryless arithmetic

Example

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

Maple

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

Crossrefs

Cf. A010888, A169821.

Sequence in context: A306004 A056992 A339023 * A004159 A092554 A155787

Adjacent sequences: A169905 A169906 A169907 * A169909 A169910 A169911

Keyword

nonn,base

Author

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

Status

approved