A169911 Primes in carryless digital root arithmetic in base 10.

3, 6, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 31, 32, 34, 35, 37, 38, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 61, 62, 64, 65, 67, 68, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87

Offset

1,1

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).

The units are {1,2,4,5,7,8}. A prime is a number N whose only factorizations are of the form N = u*M where u is a unit.

All numbers of the form 100...01 (with k >= 0 zeros) are prime, so there are infinitely many primes.

Links

N. J. A. Sloane, Table of n, a(n) for n = 1..458

Index entries for sequences related to carryless arithmetic

Example

96 has a representation 31*6 and is not in the sequence.

Maple

# carryLmult implemented in A169908
isA169911 := proc(n)
    local a, b, un ;
    un := {1, 2, 4, 5, 7, 8} ;
    for a from 1 to n do
    for b from 1 to a do
        if a in un or b in un then
            ;
        else
            if carryLmult(a, b) = n then
                return false;
            end if;
        end if;
    end do:
    end do:
    if n in un then
        false ;
    else
        true;
    end if;
end proc:
  e := 1:
for n from 1 do
    if isA169911(n) then
        printf("%d %d\n", e, n) ;
        e := e+1 ;
    end if;
end do: # R. J. Mathar, Jul 12 2013

Crossrefs

Sequence in context: A200723 A135738 A307574 * A073851 A290541 A043321

Adjacent sequences: A169908 A169909 A169910 * A169912 A169913 A169914

Keyword

nonn,base

Author

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

Status

approved