A375166 Nonsquares congruent to {0, 1, 4, 7} modulo 9.

7, 10, 13, 18, 19, 22, 27, 28, 31, 34, 37, 40, 43, 45, 46, 52, 54, 55, 58, 61, 63, 67, 70, 72, 73, 76, 79, 82, 85, 88, 90, 91, 94, 97, 99, 103, 106, 108, 109, 112, 115, 117, 118, 124, 126, 127, 130, 133, 135, 136, 139, 142, 145, 148, 151, 153, 154, 157, 160, 162

Offset: 1

Author

Stefano Spezia, Aug 05 2024

Keywords

• nonn
• easy

Comments

Squares are congruent to {0, 1, 4, 7} modulo 9, but the reverse is not always true since there are nonsquares that have the same congruence property. See Beiler.

References

• Albert H. Beiler, Recreations in the theory of numbers, New York, Dover, (2nd ed.) 1966. See p. 140.

Crossrefs

Intersection of A000037 and A056991.

Cf. A000290, A056992, A070433.

Programs

Mathematica

Select[Range[0,162], !IntegerQ[Sqrt[#]] && MemberQ[{0,1,4,7}, Mod[#,9]] &]

Python

from itertools import count, islice
from sympy.ntheory.primetest import is_square
def A375166_gen(): # generator of terms
    for i in count(0,9):
        for j in (0,1,4,7):
            if not is_square(i+j): yield i+j
A375166_list = list(islice(A375166_gen(),40)) # Chai Wah Wu, Jun 05 2025