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

1,1

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

Links

Michel Marcus, Table of n, a(n) for n = 1..74

Michael S. Branicky, Proof for A373225

Example

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.

Maple

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

Crossrefs

Cf. A096448, A373224, A373223.

Sequence in context: A158189 A218255 A256481 * A085745 A106856 A045387

Adjacent sequences: A373222 A373223 A373224 * A373226 A373227 A373228

Keyword

nonn

Author

Peter Luschny, May 29 2024

Extensions

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

Status

approved