A195375 Numbers whose cube expanded in base 14 uses only prime digits.

13, 21, 27, 693, 3587, 75285, 435365, 437155, 929509, 1731765, 1902599, 1926903, 104916853, 605497891, 1914409189, 4634485093, 12882557131, 112438392323

Offset

1,1

Comments

14 is believed to be the first base in which there are infinitely many such numbers.

Links

Table of n, a(n) for n=1..18.

Shyam Sunder Gupta, Can You Find? (CYF)

Example

27 is in the sequence because 27^3 = 13 + 5*14 + 2*14^2 + 7*14^3 uses only prime coefficients, namely 13, 5, 2 and 7.

Maple

isA195375 := proc(n)
        dset := convert(convert(n^3, base, 14), set) ;
        for d in dset do
                if not isprime(d) then
                        return false;
                end if;
        end do;
        return true;
end proc:
for n from 1 do
        if isA195375(n) then
                print(n);
        end if;
end do: # R. J. Mathar, Sep 20 2011

Prog

(PARI) isA195375(n, b=14)={n=divrem(n^3, b); until(!n=divrem(n[1], b), isprime(n[2])|return); 1}
/* The following version allows us to vary the set of allowed digits: */
is_A195375(n, a=10412/*=2^2+2^3+2^5+2^7+2^11+2^13*/, b=14)={
n=divrem(n^3, b); until(!n=divrem(n[1], b), bittest(a, n[2])|return); 1
}  \\ M. F. Hasler, Sep 21 2011

Crossrefs

Sequence in context: A304006 A304948 A087683 * A128819 A165955 A331116

Adjacent sequences: A195372 A195373 A195374 * A195376 A195377 A195378

Keyword

base,nonn

Author

Kausthub Gudipati, Sep 17 2011

Extensions

a(13)-a(18) from D. S. McNeil, Sep 20 2011

Status

approved