A393905 Square array read by antidiagonals: optimal diameter of g-Golomb Ruler of multiplicity n and length n+k, for k>=1.

1, 3, 2, 6, 4, 3, 11, 6, 5, 4, 17, 9, 7, 6, 5, 25, 13, 10, 8, 7, 6, 34, 18, 13, 10, 9, 8, 7, 44, 23, 16, 13, 11, 10, 9, 8, 55, 29, 20, 16, 14, 12, 11, 10, 9, 72, 36, 25, 20, 16, 14, 13, 12, 11, 10, 85, 44, 30, 23, 20, 17, 15, 14, 13, 12, 11, 106, 53, 35, 28, 23, 20, 18, 16, 15, 14, 13, 12

Offset

1,2

Comments

k<=0 are trivial.

References

M. D. Atkinson and A. Hassenklover, Sets of integers with distinct differences, Sch Comput. Sci., Carleton Univ., Ottawa, Ont., Canada, Rep. SCS-TR-63, Aug 1984.

M. D. Atkinson, N. Santoro, and J. Urrutia, Integer sets with distinct sums and differences and carrier frequency assignments for nonlinear repeaters, IEEE Transactions on Communications, Vol. Com-34, No. 6, June 1986.

J. Balogh, Z. Füredi and S. Roy, An upper bound on the size of Sidon sets, Amer. Math. Monthly 130 (2023), no. 5, 437-445.

Y. Caicedo, C. Martos, and C. Trujillo, g-Golomb rulers, Rev. Integr. Mat. 33 (2015), no. 2, 161-172.

D. Carter, Z. Hunter and K. O'Bryant, On the diameter of finite Sidon sets, Acta Math. 175 (2025), no. 1, 108-126.

C. Martos, D. Daza and C. Trujillo, Near-optimal g-Golomb rulers, IEEE Access 9 (2021), 65482-65489.

Links

Table of n, a(n) for n=1..78.

Aditya A Gupta, Code for generating g-golomb rulers

Example

Square array begins:
  1 3  6 11 17 25 ...
  2 4  6  9 13 18 ...
  3 5  7 10 13 16 ...
  4 6  8 10 13 16 ...
  5 7  9 11 14 16 ...
  6 8 10 12 14 17 ...
  ...

Crossrefs

Cf. A003022, A392461, A392462, A392463, A395265.

Sequence in context: A339333 A339334 A360259 * A340873 A033940 A286367

Adjacent sequences: A393902 A393903 A393904 * A393906 A393907 A393908

Keyword

nonn,tabl

Author

Aditya A Gupta, May 12 2026

Status

approved