A289667 Concatenate prime factorization written in base 3, convert back to decimal.

1, 2, 3, 8, 5, 21, 7, 21, 11, 23, 11, 75, 13, 25, 32, 22, 17, 65, 19, 77, 34, 65, 23, 192, 17, 67, 30, 79, 29, 194, 31, 23, 92, 71, 52, 227, 37, 73, 94, 194, 41, 196, 43, 227, 104, 77, 47, 201, 23, 71, 98, 229, 53, 192, 146, 196, 100, 191, 59, 680, 61, 193, 106, 24

Offset

1,2

Comments

A080670 is the base 10 version, A230625 is the binary version.

Links

Michael De Vlieger, Table of n, a(n) for n = 1..10000

Maple

# take ifsSorted from A080670
A289667 := proc(n)
    local Ldgs, p, eb, pb, b ;
    b := 3;
    if n = 1 then
        return 1;
    end if;
    Ldgs := [] ;
    for p in ifsSorted(n) do
        pb := convert(op(1, p), base, b) ;
        Ldgs := [op(pb), op(Ldgs)] ;
        if op(2, p) > 1 then
            eb := convert(op(2, p), base, b) ;
            Ldgs := [op(eb), op(Ldgs)] ;
        end if;
    end do:
    add( op(e, Ldgs)*b^(e-1), e=1..nops(Ldgs)) ;
end proc:
seq(A289667(n), n=1..30) ; # R. J. Mathar, Aug 05 2017

Mathematica

Table[FromDigits[#, 3] &@ Flatten@ Map[IntegerDigits[#, 3] &, FactorInteger[n] /. {p_, e_} /; p > 0 :> If[e == 1, p, {p, e}]], {n, 64}] (* Michael De Vlieger, Jul 29 2017 *)

Prog

(PARI) a(n) = {if (n==1, return(1)); f = factor(n); s = []; for (i=1, #f~, s = concat(s, digits(f[i, 1], 3)); if (f[i, 2] != 1, s = concat(s, digits(f[i, 2], 3))); );  fromdigits(s, 3); } \\ Michel Marcus, Jul 27 2017

Crossrefs

Cf. A080670, A195264, A230625, A230627.

Sequence in context: A346957 A062956 A333375 * A053650 A119794 A117987

Adjacent sequences: A289664 A289665 A289666 * A289668 A289669 A289670

Keyword

nonn,base

Author

N. J. A. Sloane, Jul 27 2017

Extensions

More terms from Michel Marcus, Jul 27 2017

Status

approved