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A169911 Primes in carryless digital root arithmetic in base 10. 4
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 (list; graph; refs; listen; history; text; internal format)
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: A115012 A200723 A135738 * A073851 A043321 A241858

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

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Last modified June 28 04:43 EDT 2017. Contains 288813 sequences.