A000696 Numbers k such that (1,k) is "good".

1, 7, 31, 37, 109, 121, 127, 133, 151, 157, 403, 421, 511, 529, 631, 637, 661, 679, 1579, 1621, 1633, 1969, 1981, 2017, 2041, 2047, 2053, 2071, 2077, 2143, 2149, 2167, 2173, 2401, 2527, 2557, 2677, 6493, 6559, 6643, 6661, 6703, 6733, 6871

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• base

Comments

Let S be the set of nonnegative integers whose base-4 representation does not contain the digits 2 or 3. A pair (M,N) of nonnegative integers is called "good" if every nonnegative integer can be represented uniquely in the form M*s_1 - N*s_2 where s_1 and s_2 are in S.

References

• N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• N. G. de Bruijn, Some direct decompositions of the set of integers, Math. Comp., 18 (1964), 537-546.

Crossrefs

Cf. A000695.

Extensions

More terms from Sean A. Irvine, Feb 27 2011