A069089 a(n) is the number of 0's in a p X p square of a particular function mod p (see Formula) where p is the n-th prime.

0, 1, 4, 5, 9, 16, 28, 17, 29, 52, 37, 60, 72, 73, 85, 88, 121, 140, 145, 97, 136, 113, 137, 208, 180, 216, 165, 181, 156, 228, 201, 241, 252, 249, 276, 249, 284, 321, 293, 348, 305, 392, 373, 408, 404, 337, 385, 441, 449, 460, 456, 461, 476, 461, 488, 505

Offset

1,3

Comments

Original name: Related to Lucas property of a number array.

Corresponds to the numbers z(1|1,1,1) in Razpet, Table 4, p. 163 (but note Razpet has an error for p=23). - Sean A. Irvine, Apr 03 2024

References

M. Razpet, The Lucas property of a number array, Discrete Math., 248 (2002), 157-168.

Links

Table of n, a(n) for n=1..56.

Sean A. Irvine, Java program (github)

Formula

Let p be the n-th prime and w(i,j) = Sum_{k=max(i,j)..i+j} binomial(k, i) * binomial(i, k - j), then a(n) is the number of values w(i,j) = 0 (mod p) in the square bounded by 0<=i,j<p [see Razpet p. 159 for a more general w function].

Crossrefs

Sequence in context: A278336 A051216 A255978 * A143096 A280225 A153058

Adjacent sequences: A069086 A069087 A069088 * A069090 A069091 A069092

Keyword

nonn

Author

N. J. A. Sloane, Apr 12 2002

Extensions

a(9) corrected and more terms from Sean A. Irvine, Apr 03 2024

Status

approved