A373225 - OEIS

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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

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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.