cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A169911 Primes in carryless digital root arithmetic in base 10.

Original entry on oeis.org

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

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Keywords

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.

Examples

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

Programs

  • 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

A169821 a(n) = n*n in carryless arithmetic mod 9 in base 10.

Original entry on oeis.org

0, 1, 4, 0, 7, 7, 0, 4, 1, 0, 100, 121, 144, 160, 187, 117, 130, 154, 171, 100, 400, 441, 484, 430, 477, 427, 460, 414, 451, 400, 0, 61, 34, 0, 67, 37, 0, 64, 31, 0, 700, 781, 774, 760, 757, 747, 730, 724, 711, 700, 700, 711, 724, 730, 747, 757, 760, 774, 781, 700, 0, 31, 64
Offset: 0

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Author

Keywords

Comments

Addition and multiplication are the same as in school, that is, done in base 10, except that there are no carries and individual digits are added or multiplied mod 9.

Examples

			13*13 = 160:
..13
..13
----
..30
.13.
----
.160
----
		

Crossrefs

Cf. A010878, A169908. See A170990 for a better version.
Showing 1-2 of 2 results.