A373225 Primes p = prime(k) such that 0 = Sum_{j=1..k} T(k, j) where T(n, k) = K(prime(n), prime(k)) * K(prime(k), prime(n)) and K is the Kronecker symbol.

2, 11, 23, 31, 47, 59, 67, 103, 127, 419, 431, 439, 467, 1259, 1279, 1303, 26947, 615883, 616787, 617051, 617059, 617087, 617647, 617731, 617819, 617879, 618463, 618559, 618587, 618671, 620467, 623867, 623879, 624199, 624271, 624311, 624319, 624331, 626887, 626987, 627071

Offset: 1

Author

Peter Luschny, May 29 2024

Keywords

• nonn

Comments

It appears that, apart from 1st term 2, this is a subsequence of A096448. - Michel Marcus, May 30 2024

For n > 2, the sequence is exactly those terms p in A096448 with p == 3 (mod 4); see linked proof. - Michael S. Branicky, May 30 2024

Examples

			The corresponding indices in A373224 start: 1, 5, 9, 11, 15, 17, 19, 27, 31, 81, 83, 85, 91, 205, 207, 213.
T(k, j) defined as in the name. 11 is a term because 11 = prime(5) and Sum_{j=1..5} T(k, j) = 1 + (-1) + 1 + (-1) + 0 = 0.
		

Links

• Michel Marcus, Table of n, a(n) for n = 1..74
• Michael S. Branicky, Proof for A373225

Crossrefs

Cf. A096448, A373224, A373223.

Programs

Maple

A := select(n -> A373224(n) = 0, [seq(1..500)]):
seq(ithprime(a), a in A);

Extensions

a(17) onward from Michel Marcus, May 30 2024